Volume 13 Number 4 October 1989 YU ISSN 0350-5596 Informatica A Journal of Computing and Informatics The Slovene Society INFORMATIKA Ljubljana A Journal of Computing and Informatics Subscription Information Informatica (YU ISSN 0350 - 5596) is published four times a year in Winter, Spring, Summer and Autumn (4 issues). The subscription price for 1989 (Volume 13) is US$ 30 for companies and US$ 15 for individuals. Claims for missing issues will be honoured free of charge within six months after the publication date of the issue. Printed by Tiskarna Kresija, Ljubljana. Informacija za naročnike Informatica (YU ISSN 0350-5596) izide štirikrat na leto, in sicer v začetku januarja, aprila, julija in oktobra. Letna naročnina v letu 1989 (letnik 13) znaša za podjetja 48(KX) din, za zasebne naročnike 12000 din, za študente 4000 din; posamezna številka 16000 din. Številka žiro računa: 50101-678 - 51841. Zahteva za izgubljeno številko časopisa se upošteva v roku šestih mesecev od izida in je brezplačna. Tisk: Tiskarna Kresija, Ljubljana. Na podlagi mnenja Republiškega komiteja za informiranje št. 23 - 85, z dne 29. 1. 1986, je časopis Informatica oproščen temeljnega davka od prometa proizvodov. Pri financiranju časopisa Informatica sodeluje Raziskovalna skupnost Slovenije. A Journal of Computing Informatics EDITOR-IN-CHIEF Anton P. Železnikar Iskra Delta Computers, Ljubljana ASSOCIATE EDITOR Rudolf Murn Jožef Stefan Institute, Ljubljana The Slovene Society INFORMATIKA Ljubljana Utnik 13 Številka 4 Oktober 1989 YU ISSN 0350-5596 Časopis za računalništvo in informatiko VSEBINA Synthesis in Complex Problem Domains An Informational Theory of Discourse I Assuring Numerical Stability in the Process of Matrix Refactorization within Linear Programming Package on PC Formal Verification of Distributed Systems Characterization of Circuits in Grid Obtained by Regular and Semi - regular Tessellations On the Intersection of Two Convex Polygons Fraktali - znanost ali umetnost Primena metoda inženjerstva znanja u obrazovanju Strategija računalništva Novice in zanimivosti Avtorsko stvarno kazalo časopisa Informatica, letnik 13 (1989) Some Recently Published Papers in Foreign Professional Periodicals M. Gerkeš A. P. Zeleznikar J. Bade J. Grad Tatjana Kapus B. Horvat J. Zunić /. Stojmenović D. M. Acketa Violeta Hank D. Surla Jasna Donlagić N. Guid L. Jeremić Z. Budimac Mirjana Ivanović 1 16 38 44 48 52 58 69 72 82 92 SYNTHESIS IN COMPLEX PROBLEM DOMAINS INFORMATICA 4/89 Keywords: synthesis, complex systems, abstraction, hierarchical decomposition, structuring Maksimilijan Gerkeš Metalna Maribor ABSTRACT: Complex systems' synthesis becomes a bottleneck of production process. Some researchers denote this situation as crisis, others as "crisis". However, complex systems' synthesis especially those, which cannot be implemented within particular technology domain is an open problem. The contribution gives a collection of procedures, developed with integration and some inovations of classical procedures and more advanced procedures. As a result, synthesis process can be based on abstraction, hierarchical decomposition, and structuring, while its derivation is nested in actual technological context, expressed through requests synthesized solution must satisfy. POVZETEK: Sinteza v domeni itompleksnih problemov Sinteza kompleksnih sistemov postaja vedno bolj ozko grlo produkcijskega procesa. Nekateri raziskovalci ozna£ujejo to stanje kot krizno, drug! kot "krizno". Kakorkoli, problem sinteze kompleksnih sistemov, posebej tistih, ki jih ni možno rešiti v domeni posamezne tehnologije, je dokaj odprt. Prispevek podaja skupek postopkov izpeljanih, z Integracijo in nekaj inovacijami, iz klasičnih postopkov in sodobnih postopkov sinteze. Kot rezultat lahko postopek sinteze gradimo na osnovi abstrakcije, hierarhične dekompozicije in strukturiranja, njegovo izvajanje pa je vgnezdeno v konkretni tehnološki kontekst izražen v obliki zahtev, ki jih mora izpolnjevati rešitev. INTRODUCTION Situation in high technology domains like CIM, flexible manufacturing, software, computer architectu-tes, VLSI, etc., seems similar regarding the requests for more efficient synthesis methods. For economic reasons synthesized solutions must be completely validated before manufacturing. A single error can cause exponential growth of operations to dispatch it. This calls for formal correct synthesis methods. Complexity is common characteristic of systems in the above domains. It causes an enormous amount of operations, before the synthesis goal can be satisfied. Most of the contemporary synthesis methods seem to fail because of their too close technological orientation. Rapid technology development disables efficient synthesis tools to be developed for each particular technology. Even if this Is possible, there will still remain the problem of systems implpmented in diverse technologies. This clearly calls for synthesis methods, which will be technology Independent and conceptualized on complexity and functionality issues of contemporary and advanced systems. This contribution is based on system orientation to the synthesis problem, where current technology sets limits regarding system's functionality and structure. Such an approach allows that technology based descriptions are completely avoided until the solution representation level. Altough technology sets very exact limits during the synthesis process, technological objectives are not expressed explicitly, but reflect in system structure and functionality. An approach to synthesis is used, which is based on abstract system representation transformed through hierarchical decomposition and structuring to its counterpart, the solution. Abstraction and hierarchical decomposition have long been recognized as a means, which enables complexity reduction on one side and problem decomposition to several subproblems of lower complexity on the other side. Structuring as a means to cope with complexity is more controversial and It seems there is no unisonous agreement about it. However, combining abstraction and hierarchical decomposition in the synthesis process assures only that the initial and subsequent system structures are replicated and impressed in solution system structure. On the other hand it is well known that contemporary systems are supported with an enormous amount of software, which directs their actions and is a strict consequence of systems' structuring. To visualize this we can imagine that software through execution connects an object-flow graph that corresponds to problem structure and behaviour. This means that structuring is already extensively used in system design. With respect to system represented with uncontrolled object-flow graph structuring requires three additional system structures. Its control structure directs subsystems , which can be at lowest representation level represented with uncontrolled object-flow graphs, connected in space and time. Particular strategy of , control used is of secondary importance. Its memory structure assures object validity during controlled execution. Transfer structure delivers objects to subsystems' inputs. Both memory and transfer structures are under control of control structure. Those structures are usually partitioned throughout the system following the principles of distribution and hierarchy. More intensive structuring results in complex control scheme, which is usually but not necessary expressed in a form of control code or software. Making software more close to human comprehension capabilities does not change its nature. However, it is interesting that structuring does not necessary impose any control code or software. This point of view allows that control code or software are determined as structuring side product. This is a conclusion, which sounds quite heretic, however, it gives at least theoretical possibility for automatic software development. Basic structuring concept can be explained starting wllh a system with uncontrolled flow of objects. Observe that not all resources of such a system are active simultaneously. Assume a system in which resources are disconnected and a control mechanism, which is capable to connect them in time and space. Under certain conditions behaviour of both systems can be identical. This simplified description, structuring is based on, should be completed with an observation that identical system resources can be shared when appropriate. To take advantage of this possibility system structure have to be completed with memory and transfer structures. If the behaviour of a system have to change, its control functions which determine resource connections will be appropriately modified. The simplest way to do this is through program memory, which is a part of system's control structure. Even when we look to software as problem description, system should be capable of its recognition and physical system restoration to solve the problem. A possible way to do this is that problem Is represented with problems solvable with physical system resources. However, this introduce structure that have to be implemented with physical system in isomorphic way, directly or with appropriate time and space partition. System synthesis can now be conceptualized based on the problem expressed in a form of abstract system, which have to be transformed through hierarchical decomposition and structuring to a solution, a system expressed with resources and structure that can be implemented in physical .world. Problem solvability seems to be in tight connection with Its representation. Different representations can be used to express particular view on the problem. They are equivalent In the sense that they express the same behaviour in different ways. Synthesis procedures proposed are defined for each representation. Change of one representation to another Is orderly developed. 1. OVERVIEW OF THE SYNTHESIS PROCESS Problem specification consists of two parts. Problem definition part determines an abstract system for which the synthesis process have to determine a solution expressed in the form of physical system specification to be implemented in predetermined technology domain. Behaviour of physical system can be recognized as behaviour of abstract system merely through the use of suitable abstraction, otherwise no relation exists between the systems. The rest of problem specification sets requests for the solution. Two classes, called the solution classes are determined based on the requests. Resource class consists of resource specifications, physical system should be built of. Resources determined with the resource class are generally composed and can be represented with resource structures of known behaviour. This usually allows resource class structuring through suitable relations. Abstraction through equivalence relation regarding resource behaviour reduces representation complexity and allows unnecessary details to be neglected at earlier synthesis steps. More sophisticated abstraction procedures to reduce representational complexity are described in section 3. Structure class consists of abstract resource structures. Physical system structure and its abstractions should be isomorphic to structures build of structures from structure class. Structure class is partially ordered with regard to substructure relation. Its representation complexity can be reduced through structure abstraction. Structure class can be empty. From the synthesis point of view this means that no structure requirements are set regarding the solution. Intuitively, abstract and physical systems can be delimited with the notion of distance, which is a measure proportional to the number of synthesis steps required to reach the solution. Its numeric determination provides estimate about problem complexity - P, NP complexity as the roughest measure, for example. An argument will be given to show that the synthesis problem belongs to the domain of NP - complete problems, in general. Initial synthesis steps must assure the match between problem and an abstract solution derived from solution classes. The match is found through structures' isomorphism and identical behaviour of corresponding resources. Further problem abstraction and structuring may be needed to assure it in explicit or Implicit way. It is assumed, that some generic knowledge about problem solvability in the context of both solution classes is available. In the opposite case problem can be solved with an exhaustive search only. This is probably the strongest reason why a kind of systematic frame for the synthesis process is needed. Synthesis procedures cannot be deterministic because of partial ordering of structure class. Structure limitation can play a dominant role in limiting the number of synthesis steps. The other limiting factor for the synthesis step count can be searched for in resource class. Resource class consisting of resources with simple behaviour characteristics will necessary complicate the synthesis. With proper problem structuring and composite resources built of resources from resource class this problem can be reduced. However, the effect of this depends on knowledge about problem characteristic properties. Synthesis process can be stated as a combination of hierarchical problem decomposition and structuring. Hierarchical problem decomposition is a process basically opposite to abstraction. In our case it consists of refinement and interpretation processes. With its application problem is stepwise decomposed to a structure consisting of mutually dependent subproblems each of them have lower complexity with respect to the initial problem and subsequent subproblems obtained at earlier decomposition steps. This increases problem structure complexity and causes a consequence that structures of higher problem representation levels are replicated at lower representation levels. Applying structuring to arbitrary intermediate representation level results in structure change, while preserves representation level and behaviour. Since hierarchical decomposition preserves structure and structuring preserves representation level it is clear that requirements expressed through solution classes can be met only if both hierarchical decomposition and structuring are applied during the synthesis process. Synthesis process can be recognized as partial ordering relation between problem, intermediate solutions, and solution, where the solution or solutions are those intermediate solutions, which satisfy requests expressed through botii solution classes. To find a path between -problem and solution and to avoid searching over the whole partially ordered structure of possible intermediate solutions, decisions based on their properties can drive the synthesis process. A minimal condition for an intermediate solution to be accepted for further synthesis is that it can be expressed with the objects of both solution classes. Different synthesis strategies can be used to determine the synthesis process. The simplest one and probably the less useful is one, where hierarchical decomposition to the resource class representation level is done first. This intermediate solution is then structured to assure compatibility with objects from structure class. However, structuring can become a task of excessive complexity within this approach. To avoid such situations, hierarchical decomposition and structuring are combined during the synthesis process. This assures manageable subproblems' complexity. Applying structuring and abstraction to both solution classes match between intermediate solution and structure consisted of objects from both solution classes can be found at each intermediate representation level. When such a match can be found between an intermediate solution and a structure consisting of objects from both solution classes without any abstraction such intermediate solution is accepted as a solution. Structures' isomorphism and identical behaviour of corresponding resources assure systems' equivalence. 2. REPRESENTATIONS Different views can be applied to represent the same system. In conventional one system Is represented as a structure of interconnected resources with known behaviour. For system behaviour representation it is interesting to represent resource inputs with input positions and its outputs with output positions. Positions represent perception points from which object flow is oriented toward the resource or from it. For two connected resources corresponding position plays double role. It is output position for one resource and input position for the other. Labelled bipartite directed graphs are suitable abstraction for this view on system's structure. System's behaviour can be represented with the behaviour of system resources. Based on resource positions collection of objects flowing to and from resource can be determined. Each collection corresponding to fiarticular resource has objects represented with i m -t- n tuples corresponding to objects on input and output resource positions. Such a collection can naturally be represented with function or relation, depending whether resource reacts to the same input In deterministic or nondeterministic way. Relation between functional and relational resource behaviour will be clarified later, in this section. During the synthesis process more attention can be given to system structure since its behaviour remains the same throughout this process. For this reason resource structure can be represented neglecting positions in system structure. Definition; Resource structure is labelled directed graph C = (V,E), where V = {Vj,...,/^^} is a set of resources, and E = {e^, x V is a set of resource connections. Resource labelling is defined with functions which assign labels to resources and connections and enable system behaviour recognition. Returning to the initial system model represented with bipartite directed graph it can easy be recognized that this representation is In close connection with data-flow graphs defined in Cl] , [2] . In our case modification of this definition will be used for representing system's structure and behaviour. Definition: Controlled object-flow graph is labelled bipartite directed graph C = (AULUK, E), L fi K = O, A = is a set of action nodes, and LUK ={!,,.is a set of links, where K is a set of control links. E C (A x (LUK) U (LUK) x A) is a set of branches defined so, that the following restrictions are satisfied. (a,, Ej; (a., I^)£ E =^.3, = a., (1^. a.) e E c. (1^, a.) e E a, = aj. 'k^ 'k e LUK, LUK, 1 < i, j < m, 1 < k < m + r. Two kinds of behaviour can be assigned to action nodes of controlled object-flow graph. One is represented with function, the other with controlled function. In the final case action node: must have at least one input control link. Let f: X^x...xX^—► Y be a function defined on known sets Y. Controlled function g for function f is a function. g: Bool x X^x...x X^ g (P, X,, Y, Bool = {0,1} Figure 2.1 shows controlled object-flow graphs for functions f and g. Figure 2.1: Controlled object-flow graphs for functions f and g x_) = undef n To avoid confusion instead of g(0, x^,. we can define g(0, = z, z e Y U {z) . Object z has different Interpretations in different implementation situations. In electronic systems it can be used to represent a high impedance condition, for example. In general. It represents no object or no activity situations. The notion of controlled function can be extended to more sophisticated cases of controlled execution. Examples can be found in section 5.2. One further example is provided below. g: AxX^ X ... xX^—► Y, A={a,, J g(a. Xj, 'O^v x„);a=a, ''nl = M'.....n' undef p = 0. However, it can be shown that they are expressible within the initial definition of controlled function. The notion of controlled function allows formal connection between controlled object-flow graph and control-flow graph. Definition: Control flow graph is labelled bipartite directed graph G = (QUA, E), where Q= {q,.....q^^} is a set of states, and A = {a^, ..., a^}- Is a set of function nodes. E S((QxA) U (AxQ)) is a set of branches. System's behaviour expressed through control flow graph is based on state concept. Particular state, when recognized active, fires corresponding functions. This situation is effectively modelled with a pair, consisting of decision function and controlled function, which is fired with decision function's value. Section 5 gives more detail about this topic. To allow change of representation during the synthesis process conversions between the above representations are defined. To increase synthesis flexibility they are of one - to - many type. Conversions between resource structure and controlled object - flow graph a^ based on graph Isomorphism with deleting or Inserting link nodes. However, those conversions are usually applied with structuring, what makes correspondence between structures less explicit. Conversions between controlled object - flow graph and control - flow graph are less evident. Figure 2.2 gives an example of controlled object - flow graph to control - flow graph conversion. Formal basis for those conversions is given in section 5. '2 < "l 9 "3 (O ^ ■o. Figure 2.2: Example of controlled object - flow graph to control - flow graph conversion Nodes of control - flow graph marked with lare inserted to increase readability. From the formal point of view they are not necessary. To describe system's behaviour production rules expressed with if then clauses can be used. We will show that such system descriptions can be converted to controlled object - flow graph descriptions and vice versa. Originally conditional statements are used to represent if then clauses. Take ... , x^) —► Q (y^.....y^) as an example. Define characteristic functions for R and Q, hß (x^. ... ,xj = .....''n^ RTqTTTTTiry fi; Q(yi.....yj r = h (y.....y ) = \ ^ ^ ' U; Q(y,.....yJ. Implement h^ with controlled function g^, .....yn,»' p = i ^ = Sq^P' .....^m' = ; p = 0. It can easy be verified that p, r, and q determine truth table for conditional. Corresponding controlled object - flow graph is shown on figure 2.3. controlted identical function Figure 2.3: Controlled object - flow graph representing conditional clause This representation allows inference processes' modelling in functional Way. Model of condition - action rule can be developed with slight modification of the above construction. Let R(x^, ... , x^) —»QCx^, ... , x^, y), and Q(Xj, ... , Xj^, y) (y = f(x^, ... , x^)). Define characteristic function h for R, which defines domain of f. p = h(x,, ... , x^) = ''l.....V 1 ; R(x^, ... , x^) 0 ; ... , x^). and implement f with controlled function g, p = 1 undef ; p = 0. Controlled object - flow graph that corresponds to the above construction is shown on figure 2.1. f(x^, ... , x^) Figure 1.H-. Controlled object - flow graph representing condition - action rule It is interesting to note that observing behaviour only on input and output links of a graph we are not able to Identify whether function f is implemented directly or with function g. When dealing with systems it is usually presupposed that resources behave functionally. For systems described with relational connectives the above assumption may not be true. A minor modification allows that resources, which express relational behaviour can be treated in functional or relational way depending on point of view used. Since the complete treatment for arbitrary relations is relatively extensive, we will limit this presentation to binary relation R{x,y), which is partially closed with object a, R(a,y), a b, a b i+1 a b, a b, i+n Applying object a to a resource, which behaves corresponding to R, Its response will be nondeterministic since it can delivers any object from bj, , ... »bj^^ to Its output position to satisfy R. The behaviour of a such resource can be represented in functional way, if resource response Is determined with a sequence function replacing R. Sequence function determines the order in which resource reacts with output objects to the same input determined with object a. Figure 2.5 gives tabular definition of sequence function and corresponding controlled object - flow graph for this case. f: a ''i "i+l a Vi a "i.n Figure 2.5: Tabular definition of sequence function and corresponding controlled object - flow graph Identifiers 1 through 5 stand to Identify functions fork, decision Boolean functions, controlled identical functions, function join, and memory function. Functions fork replicate input objects, decision Boolean functions control corresponding identical functions to deliver particular object bj^j to function join, which is a tres-hold function and delivers object bj^j to output link. Memory function assures necessary delay. Assumption is made that y**"' has allways a value from Two notes are necessary about the above presentation. First, It is simplified to serve conception presentation only, and second, sequence function can be defined In a number of different ways. 3. REFINEMENT AND INTERPRETATION Using abstraction representation complexity can be reduced to a manageable level. During the synthesis process the situation is reversed, complexity grows, since this process is basically opposite to abstraction. Assume a solution system represented with resource structure and resource behaviour. Using a substructure relation to determine an arbitrary substructure observe that its behaviour can be described with collection of objects which correspond to its input and output positions. This enables that substructure is replaced with a resource having input and output positions that correspond to substructure input and output positions. The replacement causes lower system structure complexity- Representing the system in each possible way with replacing substructures with resources while preserving their input output behaviour results in a class of systems with different structures and the same input output behaviour. An important hypothesis can be made at this point. System structure abstraction has sense only if the substructure behaviour can be expressed with its input output behaviour'. Represent collections of objects which determine resources' behaviour with tables and assume they are of finite leught. Resource behaviour is represented with single table, while resource substructure behaviour is represented with a structure of interdependent tables. Select a pair resource, resource substructure with identical behaviour. The question arises whether the structure of interdependent tables can be developed based on the information obtained from single table. Results of empirical study show that this is possible. However, for a formal proof of the above claim additional research is needed. Results of mentioned study show that refinement based on the above concept is generally NP - complete problem since lower complexity bound grows exponentially with the number of table entries in non - trivial cases. Refinement is nondeterministic process that can be automated. Automatic algorithm development is possible. Controlled functions are necessary to obtain all possible refined versions of particular function. Refinement can be done on uncompletely specified tables. If this causes a lose of significant information, obtained algorithm will not be optimal. Example 3.1 gives tabular refinement for selected case of binary addition and corresponding controlled object - flow graphs, which have no control links for this case. Only one path of the whole refinement process is presented. Example 3.1 Loops and circles in resource substructure can introduce additional substructure inputs and outputs which are local to it. f: "l ®o ''o =2 ^0 0 0 0 0 0 0 0 1 0 10 0 0 10 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 10 0 0 11 0 110 0 111 0 0 1 0 1 0 0 1 1 1 0 0 10 0 0 10 0 1 110 0 110 1 0 1 0 0 1 1 1 0 0 1 0 1 10 10 10 11 1110 1111 0 1 1 1 0 0 1 0 1 110 G: Table T represents binary addition decompose to tables T^, T^, and Tj, what results In the following controlled object - flow graph. "l «0 ^ l.step I 2.StEp 1 u 0 0 0 1 \ H)--«— 1 1 0 1 1 >1 1 1 -e—e—&- -e—e—1- H—6—0- —e—1- -«-H—9- -G—1-1- H—1—8- H—1—h- '11 • '11 a« 0 0 ''o 0 0 0 0 1 1 1 0 1 1 1 0 T^ becomes T^^ after deleting redundant entries. Corresponding controlled object - flow subgraph Is reduced as represented below. t>. '32 '21 ■ 22' '21 0 0 0 0 0 0 1 0 1 0 0 1 1 1 '22 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 T^ is decomposed to T^^ and Tj^. Corresponding controlled object - flow subgraph is refined as represented below. '32- ^=2 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Controlled object - flow graph obtained after refinement of T^, Tj, and T^ is given below. Because of close relation between tabular and expres-sional function representation, the former can be thought of as tabular structure abstraction. Refinement procedures are generally developed for expressional function representation. Since this type of refinement is widely i^nown its presentation will be avoided. 3.1 Function refinement This subsection states conditions that have to be satisfied with function refinement. Figure 3.1 shows graph of relations and controlled object - flow graphs for functions f and g, which is composition of functions g^. ••• / g^ obtained through refinement. Refined function g and Initial function f have to satisfy the relation f = o g o h^ = g, and h^ functions. h2 are identical Refinement of Tj is analogous to the refinement of Tj. The result is. ■^31 = "^21 ' A^x ., A^x ., . x A_ . x A_ B,x ... x B^ B.x ... x B Figure 3.1: Function refinement Dependent of actual representation defined in section 2 function refinement is completed with corresponding graph refinement. Procedures for them can be found in [2] , [3] . Refinement can be thought of as a case of interpretation. However, we will give only basic definition and neglect this possibility. Figure 3.2 shows graphs of relations and corresponding controlled object - flow graphs when Interpreting function f with function g. When interpreting function f with function g the relation f = h~' o g o h^, where h^ and h^ are surjec-tive and possibly partial functions must be satisfied. Functions h^ and hj assure compatibility with the environment. They can be stepwise removed with interpretation of environmental functions. Since h~ is generally relation this can cause formal inconsistency with controlled object - flow graph behaviour. Since h^' can be represented with sequence function as illustrated in section 2 this can cause no serious problems. On the other hand h^^ and h^ can be stepwise removed as mentioned above. The inconvenience can be avoided when h^ is bijective. 3.2 Object interpretation and refinement Until now objects were considered as integral units. However, for the reason of efficiency such observation is too restrictive. To avoid this, object representation can be adapted to problem representation level. Intuitively, an arbitrary object composed of several objects can be viewed as integral unit or as a structure of objects positionally^ determined. In first case the fact that object is composed is neglected. Several objects must satisfy some known relation which determine their mutual positions to be recognized as integral unit . To represent such structures n - tuples are used. Object refinement and interpretation^ore defined in connection with corresponding system's functions. Figure 3.3 shows a graph of relations and corresponding controlled object - flow graphs when refining objects of function f with objects of function g. -A^x C,x x A x C m B,x D,x x B x D B A,x ... x A„-» B.x ... x B_ 1 ml n a O a o- 1. More than simple resource can be controlled with a decision function and consequently more resources can be controlled with state transition function as mentioned earlier. A pair decision function, controlled function enables structuring. A set of such pairs which determines the system can be partitioned to disjunctive subsets. The same effect can result from system partition on the set of disjunctive subsystems. System integration based on its arbitrary partition can be realized in more different ways. Before do this we have to develop object transfer functions and memory functions. Transfer functions realize object transfer between positions, while memory functions assure that objects retain particular positions so long as determined with control structure. 4.1 Transfer functions Flow of objects between two arbitrary subsystems separated with a partition can be implemented with selecting and distributive functions. Assume a subsystem which has to be connected to another subsystem over positions p^, ... . p^^. Denote sets of objects corresponding to positions with X^.....X^, and let X = X, U ... U X^. Selecting function "M is defined as. TT : N x Xj x ... x X^- i(i, x^, ... , x^) = x., 1 < i ^ n undef, otherwise. The set of natural numbers N above can be replaced with arbitrary linearly ordered set. Indexes of x^, ... , x^ become objects of such set. Linear ordering can be avoided If selecting function is defined in tabular form. Both approaches to define selecting operation can be mixed. Levels of indirection can be built to the alcove definition to determine particular position of n-tuple. Figure 4.2 shows controlled object - flow graph of selecting function. subsystem sufficient to Implement arbitrary connection between two subsystems. They can be decomposed and expressed with controlled function defined in section 2. a.2 Object representation in recursive domain Let X be a set of objects to be represented in recursive domain. This representation is achived with function. f : N x X Figure i».2: Controlled object - flow graph of selecting operation Distributive function delivers objects obtained from selecting function to prespecified positions of a subsystem. Distributive function is defined as, 5 : N x X y, x ... x yn, (y,.....yn,J= 5 (undef,...,x, ...,undef) ,yj=x, Ki 1 and p = 1 for particular i only, y have the value of x', if i+k < n^. Extension to represent an object in time domain Is straightforward and will not be considered here. Selecting and distributive functions can be composed to realize arbitrary complex networks, which are capable of transfering specified amount of objects in time and space. More requests for transfer than transfer paths available can exist simultaneously. Such requests are paid with appropriate time - space partition of transfer. Selecting and distributive functions are not the only transfer functions possible. However, they are 1.3 Function representation in recursive domain System's behaviour can be represented in recursive domain when its functions are transformed to this domain. Similar extension in representation can be developed for time domain, continous or discrete. This allows synthesis in time domain. Recall a no object situation described in section 2. Y be a function to be Let f : X,x ... X X„ I m represented in recursive domain. Define object interpretation functions. h, : N X X, X ... X X„-1 1 m X, x ... x X 1 m h, (i- ''i.....''n^ = t^l'' ■■■' Represent (i, with ------and define (X,,..., xj; i < n^ undef ; othiervvise. ^ (''l..... "m' = hj : N X Y h, (i. y) = y' Represent pair (i,y) with y' and define. hj (y'l = y ; n^ < i < n^ undef ; otherwise. Function f can now be represented in recursive domain with function g. g : N x X^x ... x X N x Y g (i, X,.....x^) = (i+1, y) or, i+1 9 .....''In' 9 e^i.....= = y .....'^m' ' < i < "2 undef ; otherwise. Function value Is determined with i+1, while domain values are-determined vyith I. This assures memory property. In fact, function g is a composition based on function f and memory function. If defined as controlled function its value can be retained arbitrary long. Figure t.l shows controlled object - flow graph for such case. *o/' Figure <».1: Controlled object - flow graph for controlled implementation of g With the above developments we have minimal tools to define basic structuring concepts. 4.4 Distributive structuring Assume a system determined with the pairs decision function, controlled function at an arbitrary level of representation. Define a partition of pair set. Each subset of the pair set determines a subsystem, unconnected in general. Define at least one input and at least one output position for each subsystem. Select two arbitrary subsystems and determine all connections between them with regard to unpartitioned system. Between subsystems define transfer functions to reconstruct connections determined with unpartitioned system. At this point representation should be changed to recursive domain In general, since resource sharing is introduced. A sketch of the above development is shown on figure 4.5. subsystem 1 subsystem 2 O-O-O- •O fK> r*0 connections to be Implemented between subsystems copy of subsystem's state Figure 4.5: A sketch for subsystem connection The process of developing connections is repeated for all subsystems. Analogous approach Is used to develop connections with the system environment. With the insertion of transfer functions which are compositions of selecting, distributive and memory fuctions additional system states are introduced. Decision function which controls particular resource should take this into atcount to retain compatibility. Distributive structuring results in a system organized around more or less tightly connected subsystems and preserves the behaviour of the initial system. Figure 4.6 shows a simplified example of a system distributively structured. 14 copied positions apparent Note; Control structure Ì5 not shown. Figure 4.6: Example of distributive structuring 1.5 Hierarchical structuring Assume a system represented with a set of pairs decision function, controlled function. Define a partition, such that each subsystem determined with it is connected. Determine a copy of all those positions, which with the system partition decay to input and output positions. Those positions are actually subsystems' input and output positions. Each copied position will be during structuring process connected to corresponding subsystems' input and output positions. For each pair consisting of input and output positions determined with the partition and corresponding copied position define transfer function, which enables object transfer from output position over copied position to input position. To connect two subsystems over corresponding copied positions a composition of selecting, memory, and distributive functions is generally needed. Since objects on copied positions represent system's state at higher level of representation than the initial representation level the behaviour of hierarchically structured system can be interpreted in the context figure 3.5. Transfer functions can namely be completed with object abstraction and interpretation functions. This assures compatibility in representation levels. The approach to hierarchical structuring can be upgraded to state hierarchy, which is similar to memory hierarchy in contemporary systems. Similar as with distributive structuring transfer functions introduce additional system's states. Because of this decision functions, which control the execution must be appropriately modified. Figure H.l shows a simplified example of hierarchically structured system. states Figure it.7: Example of hierarchical structuring Both structuring techniques can also be applied on system's control, transfer, and memory structures. Distributed and hierarchical structuring can be combined and applied at arbitrary system representation level. As far as recognized, the proposed structuring techniques are sufficient to model arbitrary system architecture. They were developed for all representations given In section 2. To structure a system in particular representation this can be done without representation change. Since structuring allows resource sharing, system's synthesis can respect cost and performance requirements. Based on the given approach to structuring system's synthesis and software development cannot be separated since they are tightly connected with structuring. This gives at least theoretical possibility for automatic software development. On the other hand highly structured systems can be developed without any control code or software in the usual meaning. 5. CONCLUSION Review of system's synthesis process is given. Since this topic is very extensive this presentation is focused on these domains estimated as significant. However, domains determined with real - time, fault tolerance, and intelligent behaviour paradigms were completely avoided in the presentation. This does not mean that systems from these domains cannot be developed within the proposed context. In contrary. some significant practical results were obtained in the synthesis of hard real - time systems and fault tolerance in the domain of industrial process control systems. At the same time It was shown that structuring is still very controverse notion with diverse span of significance, although it is more or less clear that hard real - time and fault tolerance paradigms "are of little use in lousy structured domains. Similarly, fault tolerance cannot be a compensation for poor system design. Those were some of the reasons why structuring was given such attention in the presentation. Since it becomes more clear, that differences caused with separate development of software systems, software engineering, artificial intelligence, knowledge engineering, etc., are caused mainly because of diverse views to problems and that their solution can only be achieved with multidisciplinary approach, latest efforts to avoid such situation result in systems engineering approach. Based on this approach, systems which are capable to learn particular behaviour, analyse It and construct systems that behave equivalent can be synthesized, based on the proposed approach to the synthesis process. 6. REFERENCES K.M. Kavi, B.P. Buckles, U.N. Bhat A Formal Definition of Data - Flow Graph Models, IEEE Trans, on Computers, p. 910-948, No. 11, Vol. C-35, Novt 1986. K.M. Kavi, B.P. Buckles, U.N. Bhat Isomorphism Between Petri Nets and Dataflow Graphs, IEEE Trans, on Software Eng., p. 1127-1131», No. 10, Vol. SE-13, Oct. 1987. M. Gerkeä Structures and Models, Resource Interconnection, Functional Behaviour, and Control, Report, Metalna, 1988. M. Gerkeš Funkcionalno modeliranje sistemov. Strukturiranje, Poročilo, Metalna 1988. AN INFORMATIONAL THEORY OF DISCOURSE i INFORMATICA 4/89 Keywords: discourse, discursive environment, discursive process, formalization, information, informational abstraction, informational algebra, informational theory, Lacanian discourse Anton P. Železnikar* The research of the discursive nature of information, as determined in [10] and later on in [3, 4, 5, 6], is offered as the property of informing, counter-informing and embedding of information, as its spontaneous arising and cyclicity (circularity). Then, in this respect, informational phenomenology of discourse can be studied as an inherent property of information itself and, afterwards, also as its particularized form, such as is, for instance, the construct of Lacanian discourse. This part of the essay brings a general study of discourse as informational phenomenology and projects this phenomenology onto the Lacanian model of discourse, which is composed of university, master's, hysteric's and analyst's discourse. In the second part of the essay pseudo-Lacanian and other models of discourse will be studied. Informacijska teorija diskurza I. Raziskava diskurzivne narave informacije, kot je bila opredeljena v [10] in kasneje v [3, 4, 5, 6], se ponuja kot lastnost informiranja, protiinformiranja in vmešCevanja informacije, kot njena spontana nastajalnost in cikličnost (cirkularnost). Informacijsko pojavnost diskurza je tedaj mogoče preučevati z gledišča inherentne lastnosti same informacije, kasneje pa tudi kot njeno parti-kulariziranp obliko, kot je npr. konstrukt lacanovskega diskurza. Ta del spisa prinaša sploSno obravnavo diskurza kot informacijske pojavnosti in projicira to pojavnost na model lacanovskega diskurza, ki ga sestavljajo univerzni, gospodarjev, histerikov in analitikov diskurz. V drugem delu spisa bodo obravnavani psevdo-lacanovski in drugi modeli diskurza. 1. INTRODUCTION ... disagreement [difference] is the essence of communication. The aberration of sciences ... is that they see the essence of communication in the proper understanding. Jacques-Alain Miller [1] 41 The term discourse might be understood as personal or interpersonal communication or informing in acts of expressing, talking, uttering, analyzing, conversing, hearing, performing, writing, gesturing, mimicking, signaling, thinking, imagining, etc. In this Iskra Delta Computers, Development and Production Center, Stegne 15C, 61000 Ljubljana, Yugoslavia, Europe (or privately: Volaričeva 8, 61000 Ljubljana, Yugoslavia, Europe). respect a discourse concerns messaging as well as reception in individual as well as in interindividual arising, exchange, or mediation of information. The discourse can be seen as composed of three parts : the Informing of transmitter (informational arising within an informational source), informational mediating (informational propagation or in fact operation between an informational source and informational sink), and informing of receptor (informational sink) considering propagated information. In principle both - the transmitter and the receptor - have the roles of producing and accepting information. But, this is only one side of the meaning we can globally impart to the term discourse. The other side of the meaning has still to be sought in discourse's archaic foundation, i.e. in its Latin origin of the verb dis-curro and the noun discursus. For our further investigation of possible informational scenarios of discourse the Latin origin of dis-curro and discursus may not be only helpful but also conceptually relevant. The Latin dis-curro has several meanings. It means, for instance, to be full of vivacity (in our terms, to be full of informational enterprise or of enterprising informing), to be in high or great spirits, to cause great mirth or to overflow with mirth, or shortly to play, game, perform, animate (inform) spontaneously, according to a being's throwness into a life situation. It means also to disperse, scatter, run different ways, run about, to and fro, to be out of the course, however, returning to it, etc. The Latin discursus has similar meanings. The modern noun discourse means talk, conversation, discussion, chat, dialogue; speech, address; analysis, dismemberment; soliloquy, monologue, colloque; etc. Further, individual or interpersonal communication may be marked as discursive if it is based on commonsense or logical analysis, discursive thinking or cognition; discursive may mean also notional, logical, deductive, scattered, concentrated, and intuitive. Information, as being defined in [10], is also a discursive phenomenon; simply, information is discursive, it possesses its own informational discursiveness. The question of informational 'theory of discourse can concern also epistemological problems, for instance, how a particular discourse represses the truth and perverts the reality. By way of this particular example, we can enter into the domain of the so-called Lacanian types of discourse studying several Lacanian schemata or scenarios of discourse from the informationally theoretic (symbolic, logical [3, 4, 5, 6]) point of view. Certainly, before entering into discursive particularities, we can develop a general theory of discourse which can be particularized into any imaginable form of discursive behavior on the individual and interpersonal level. The basic question is how does a discourse perform informationally or what kind of informing does it perform. Within this context various general and particular scenarios can occur, opening several horizons of possible informational interaction. A GENERAL DEFINITION OF DISCURSIVE, NON-DISCURSIVE, AND ALTERNATIVE ENVIRONMENT . . . the subject of the unconscious in the Lacan's sense is nothing else than the subject of the marker, this is the scientific subject, which is however marked out in a scientific domain as a discursive subject. This is the subject being always carried by a marker. cyclic, and parallel-cyclic case of discourse, respectively: Jacques-Alain Miller [1] 64 For the sake of systematics it is possible to distinguish four characteristic cases of discursive and non-discursive environment, which are the following: discursive, non-discursive, .alternatively discursive, and alternatively non-discursive environment. For these cases four types (sets) of characteristic informational operators can be introduced, concerning the so-called general, parallel. SN- sh. s|h. 1=, 'I It^, i h, H, Ih, IK Hl, HI It is to point out that all these operators are understood to be particularly discursive or non-discursive, respectively. 2.1. A Discursive Environment In a general case of discourse we can suppose that several informational sources communicate with several informational sinks or, even more generally, that several informational entities communicate among each other. In a free discourse, where m partners are informationally involved, the basic formula of the discourse can be simply DE. «m ^ «1 This formula represents an informational system consisting of (m by m) parallel informational formulas (informational processes). DS. IN ct'i; 11= «i' «1 IN «2 «, IN «, txi IN «, •m' «m' «m «1'- «m «2'- ••• «m «m The parallel informational operator |1= means that the process to which ||: belongs can inform each process and can be informed by each process of the system in a parallel way. Simultaneously, also means that the process to which it belongs can inform in parallel within itself. If a parallel informational process is formally decomposed, its components can inform explicitly (through explicit parallel informational operators) each other in a parallel way. The parallel informational system DS shows how a discursive environment DS becomes a net of parallel marked processes. If DS is the metamarking system for DE, then DE is the metamarking discourse (i.e. informational formula) for a "realistically" comprehended act of discourse, etc. In this sense the marking nets on certain levels (or metalevels) are additionally perplexed and conform an integral marking net of understanding of the discourse. In this way, the science of discourse becomes a characteristically marking net within which this science arises and causes changes and arising of the marking net itself. For a parallel process (PP) a |N ß the following definition can be introduced: PP. (« IN ß) =Ef (((3{T IN 8)).(a IN p; T IN S)) v ((a|Nß) 'is_parallel_in_itself')) This definition can be read in the following way: a |N ß is a parallel informational process 18 iff there exists a parallel process Y IN S such that a 1,: ß and f Ir S belong to a parallel informational system (which means that they interact in parallel with each other) or a ![= ß is parallel (informs parallel) in itself. In a discursive informational environment DE, informational actors a^, «j, ••• i spontaneously communicate among each other and informationally create cultural (ontological) and individual (metaphysical) forms and processes of information. This is the most general informational model of social discourse as a phenomenon among individual parts (lumps) of a living population. Informational actors impact several actors and are impacted by several ones. The scheme of the parallel discursive system DS shows these possibilities. The general theory of discourse assumes that within a discursive system the processes of informing are spontaneous, for instance, in the sense of autopoietically structured and organized systems (informational entities). Spontaneity of informing holds on individual as well as populational informational level to the extent to which existing (currently dominating) individual and social informational processes condition and enable various informational modi. In parallel, the similar can be said for the so-called informational cyclicity. In principle, informational processes are circularly structured in their nature of informational arising. The arising itself is a spontaneous and circular process of coming of information into existence. If it is assumed that DS is in principle informationally spontaneous, the question has to be answered how could a DS formally reflect the so-called informational cyclicity. We can set the following definition for a cyclic process: CP. (oc h ß) =D£ ((0{ß 1= a)).(a 1= ß; ß ^ a)) V («, ß 'are_cyclic_in_themselves')) This formula is read as follows: « h ß is a cyclic process, iff there exists a reflexive process such that processes a [= ß ß t= <* belong to an informational system or a and ß inform cyclically within themselves. To explicate both - the parallelism and the cyclicity of a DS - an appropriately structured informational operator can be introduced and thus DS can be transformed into the formally adequate form DS-. a^ II- Ih a2; ... Ih a^^; «2 «1' «2 «2' «2 informationally interwoven situation in which the processes involved can mutually impact and can be impacted in an arbitrarily imaginable and complex manner. After this discussion it is possible to represent the general formula of discourse in the form GD. a t= ß where is a particular informational operator of discourse and where a and ß represent arbitrary informational sets of informational entities i.e. operands and/or formulas, for instance, t), ... , These entities can be formulas of informational operators and operands, etc. The point of GD is that |= is not a general informational operator but operator of discourse and that a and ß are operands being in a discursive relation. Thus, a |= ß is not a general informational formula but a particular formula concerning the act of discourse. 2.2. A Non-discursive Environment What happens if informational entities are not in discursive relation? It is certainly possible to express this fact by particular operators giving them the meaning of non-discursive nature. Some problems may occur in defining the so-called non-informational operators, where it is necessary to say explicitly which kind of particularity belongs to a particular operator of non-informing. It is possible to repeat the previous definitions of discursive environment for the case of non-discursiveness of informational processes. Dually to DE, it is possible to say explicitly that several informational entitles do not communicate among each other. The basic formula of a non-discursive environment could be in general NDE. «m ^ «1 This formula represents an informational system consisting of (m by m) general informational formulas of non-discursive informing. NDS. «1 fc^ «m' "2 ^ «m' «m «1' «m «2' • • • «m ^ % «m «1' «m «2' ••• «m ^^ «m This system may represent a particularly non-discursive environment, where for a case of non-discursive relation ^ it is possible to determine For a process a If- ß there is the following definition: PC. (a Ih ß) ((a IN ß) A (a I- ß)) This definition says that the process « |h ß informs parallel and cyclically iff it informs in parallel and simultaneously cyclically. This form of the process offers a rather complex and ND. (a ß) (n(3(a, ß)).(a |= ß)) In a similar way it is possible to determine non-discursive relations (informational operators) for cases of parallel, cyclic, and parallel-cyclic processes, respectively: NPP. (a ß) (-.(3(a, ß)).(a 11= ß)) NC. NCP. C0£ 1/ ß) (n(3(a, ß)).(a h ß)) (« W ß) (n(3(a, ß)).(a F ß)) These cases complete the philosophy concerning the so-called simple or non-alternative cases of discursive and non-discursive processes. If entities a and ß are in a process of alternative discourse, the formula AD. (a ß) V (ß a) means that a informs discursively ß in one or another way or that ß is informed discursively in one or another way. 2.3. An Alternatively Discursive Environment 2.4. An Alternatively Non-discursive Environment Let the alternatively discursive environment be introduced by saying that in case of a discursive process the act of discourse can happen in one or another way. This means that the possibility of one or another way has to be introduced operationally into formulas describing processes of discourse. One way of discursiveness was presented by the distinguished set of operators and ||-, and their counterparts (t^, and denoting the property of non-discursiveness. The other way of discursiveness can be presented by the set of 'opposite' discursive operators =j, 4/ Hand -||, and their counterparts "11' denoting another way of the property of non-discursiveness. Instead of a simple discursive environment DE it is possible to explicate the alternative environment by the system ADE. «1- «2' ••■ ' «m ^ "l' «2' ••■ ' "m- «m «1 This system says that informational sources and sinks a^^, ttj/ ■.■ i cc^^ communicate among each other in one or another way (=j) . If this communication occurs in a parallel way, the parallel decomposed system is ADS. «J^ otj^; a^ Ih «2; • • • lt= a, IN a, ; a, 11= a. «2 IN % «1' «m «2' a3_ 4 «j^; m «2,«, 4 a,; a, 4 a,; «m «m'-«1 «9 =11 «m' «m =11 «!'• «m =<1 «2' ••• «m «m Similarly to PP, CP, PC, and GO it is possible to define the following alternative cases, respectively: APP. ACP. APC. AGD. (ß a) (((3(8 4 T)).(ß Hl «; Ml T)) V ((ßm«) 'is_parallel_in_itself')) (ß H «) =Df ■ (((3(a =j ß)).(ß =i a; a =1 ß)) V (a, ß 'are^cyclic_in_themselves')) (ß HI oc) ((ß HI «) A (ß -I a)) ß =1 « Which kind of environment is alternatively non-discursive? Does a kind of totally non-discursive living environment exist at all? It is possible to construct such an environment abstractly, however only particularly, that is by introducing particular types of non-discursive operators. One kind or particularism of non-discursiveness does not mean that there does not exist or arise another type of discursiveness of the observed informational (discursive) entity. We have already pointed out some typical dilemmas of non-informing (non-discursiveness). Dually to ADE it is possible to explicate the so-called alternatively non-discursive environment by the system ANE. ••• ' «m «1' «2' ••• ' «m' ... - «jj^ «!< «2' ••• ' «m This system says that informational sources and sinks a^, «2' ••• ' "m communicate among each other in any way (neither |= nor =j). This kind of non-informing can be expressed by the marking net of the form ANS. «1 fe^ ot^; fe^ «2; ... «j^ ti (x^; «2 M «1; «2 I'' «2' ••• «2 ^ «m'- «m «r «m ^ «2' ••• «m «m' ^ "l' «1 ^ «2' • • • oc^ fij «jj^; a.^ ^ ccj^; «2 ^ «^i . . . «2 «n,; «m «1' «m «2' ••• «m «m It is important to stress that operators (in fact metaoperators ) ^ and in distinct processes of the system ANS can be marked by mutually different operational particularizations, i.e. by operational markers which mark different acts of non-discursive informing. In this manner each alternatively non-discursive environment is non-discursive only to the extent of certain particularities, and thus can never be absolutely or totally non-discursive. This can be immediately understood on the formal or on the marking level, if metasystem ANS is particularized in the following way: «1 «1 Mp a2; "2 n *2 i^iA "2' • «1 I^Y "m'- • «2 ^v ®'m' «1 4 «2' •■ «m «1' "'m ^ «2' «m «m' «1 «2 '^v «m^ «m % A particular non-discursiveness of a process has the meaning of non-communication or of the lack of a particular understanding among distinct informational entities. It seems to be important to have explicit possibilities for the expression of different forms concerning non-understanding in discursive processes. Similarly to ND, NPP, NC, and NCP, it is possible to define the following alternative cases, respectively: AMD. (ß ?i| a) (n(3(ß, a)).(ß H «) ) AMP. (ß P^l a) (n(3(ß, a)).(ß a)) AMC. (ß «) (n(a(ß, «)).(ß H «)) AHCP. (ß a) (n(3(ß, a)).(ß H| «)) This completes the discussion concerning the alternatively non-discursive environment. 3. DISCOURSE AS INFORMING IN ITSELF It is possible to postulate anything, however, the value of the obtained mathematics will be showed by its applications. Zvonimir Šikić [2] 32 3.1. General Informing within a Discourse of an Informational Entity What is in fact a discourse in itself? Is it a sort of communication in which an informational entity communicates with itself or, more precisely, informs itself? Already in the discursive system DS formulas of the form a |= a appeared; do they represent the process of discourse in itself? If so, then it would be possible to decompose the process a |= a in at ■ least two components which would mark the "speaking" component against the "addressed" one in this process. It is certainly possible to suppose that an informational entity is always in the relation to be discursive in itself or to itself. This fact could simply denote the nature of information and its informing as living, artificial, or cosmic phenomenology. The discursive nature of informational entity a could be logically postulated by the formula or system of two simple formulas, i.e., DNa. (a S=) V (1= a) a a or The meaning of this formula is that a informs and/or is informed discursively. Within this formula, appears as a unary informational operator of discourse, which in a concrete situation can be adequately particularized, to mark the desired case of discursive informing of the entity a. It is possible to say that formulas a |= and |= a are discursively open formulas. In general, formulas using unary operators are always particularly open or generally unclosed. Formula and system in DNa can be even more general, if it is said that a informs and/or is informed discursively in one and/or another way. In this case the basic discursive nature of entity a can be expressed as GNot. (a t=) V (1= a) V (=1 a) v (a =1) or a [=; 1= a; a; a ^ This case argues the introduction of the symmetric discursive operator The conditional (implication) of formula DNo is certainly CNa. ((a 1=) V (1= «)) (a N a) respectively. This formula or system characterizes the entity a as to be discursive. If, in general, information a discursively informs or is informed, then information a is in. a discursive relation to itself. However, this does not mean that information a is not simultaneously in a discursive relation with other information ß, i.e., CNß. ((a t=) V «)) ((« 1= ß) V (ß t= a)) If, in general, information « discursively informs or is informed, then it is possible that information « informs other information ß or is informed by other information ß. The operator denotes the so-called possible conditional case. 3.2. Counter-informing within a Discourse of an Informational Entity The next question of the self-discurđive process a f= a can be the following: how does information a discursively inform itself? In a discourse, information a arises as counter-information w, which has to be embedded into the source or originally existing information a. We can simply say that in a self-discursive game (informing), the discourse within o, marked by S^, arises or develops as its own counter-discourse S^, embracing counter- informational components £ and to. This counter-discourse has to be discursively embedded by into the original discourse S^. Up to now the only scended formula of a self-discourse was a a. It is possible to connect the so-called classical informational components, i.e., information a, its informing 3, counter-informing (E, counter-information w, informational embedding S, and embedding information t, with discourse counter- discourse Sy, and discursive embedding 8^. It is possible to postulate the following system of equivalences : D«. S^ S (a t= a); B = (S ^ K) N e discursiveness and informational embedding concerning the discourse as a whole will be formulated in the informationally cyclic form in section 3.4. Between the discursive and informational components the following correspondences can be observed: 3.3. Informational Embedding within a Discourse of an Informational Entity DccR. a, 3; S^^ (2, to; S^ E, e How is it possible to postulate the process of the counter-informing CC by which the counter-information w is coming into- existence? How does this process begin to arise? Let us introduce two particular informational operators for marking the looming (bursting) of this process in one or another way: lÄw. (a a) L (a L E; E J a; £ L co; (0 J <£) This system of four processes in the second line has to be understood as the beginning of the arising (operators L and J) of counter-discourse S^ (i.e. (E, w) out of discourse S^ (i.e. a ^ a). Certainly, the process of counter-informing (E has its beginning (looming). The last formula can be read as follows: the discourse a ^ a looms the counter-discursive processing (£ and in parallel (simultaneously) CC looms the counter-information w in one or another way. In fact, these four processes constitute the parallel counter-discursive system Š^. To stress the parallelness of these processes after the looming of £ out of ot and after the looming of w out of E, in the next step the following (discursively regular) formula can be introduced: PCCw. = ((« h a) IN (a Ih E; C ot; C |t= U); w =|| CC) ) It is possible to interpret the operators L and J in the primordial process LEw as particularizations of the parallel metaoperators IJ: and . respectively, The last formula, can be read in the following way: the discourse a ^ a informs the counter-informing E in parallel in one or another way and the counter-informing E informs in parallel the counter-information w in one or another way. It can be seen that in these processes there are not processes which could constitute the condition of the so-called discursive cycle. So, the process of counter-discourse is discursively open. It only means that further discursive (informational) processes have to be added to the given system to establish the circumstances of discursive circularity. It is even reasonable to join the counter-looming and counter-informing system in a unique counter-discursive system, for looming of counter-discourse .is' a steady process within a flowing process of discourse. More formulas in such a system only means that more particular information concerning discourse is on disposal. The complex game of counter- The next question which arises is what to do with the so-calléd counter-discourse or how to bring it into the context of a developing discourse. The "interest" or intention of a discourse could be to capture meaningfully as much as possible of the arisen counter-discourse, with the goal to get some origins for further development of discourse. It seems reasonable to separate or decompose this particular process of embedding, which arises in the dynamic- environment of the developing discourse. Discursive embedding, marked by S^ is a part of the so-called discursive cycle. This cycle can be formally expressed in the following way: DCto. 1= V N ^ This formula is important for the understanding of the S^'s role when S^ produces the so-called embedding information e, by which counter-information w is informationally embedded or connected to the source information a. Certainly, embedding information e does not necessarily offer the complete embedding or connectedness of w in regard to a, but ensures that counter-informational result w is not lost in the process of discursive informing. Discursive embedding as informational phenomenon underlies the process of looming of the embedding discourse and its regular continuation, for instance, in the form of an adequate parallel informational system. First, the following process of the looming of discursive embedding can be assumed: LCe. ((a 1= a) L (a LE; EJ a; E L w; w J E)) L (co L (S; e J w; C L s; E J (g) This system with four processes in the third line has to be understood as the beginning of the arising of the embedding discourse (i.e., E,' e) out of discourse S^ (i.e., C,. co), when S^ begins out of S^^ (i.e. , a a). The last formula can be read as follows: the discursive process a a looms the looming of the counter-discursive process, where counter-informing E is loomed in one or another way by information a and counter-information w is loomed in one or another way by counter-informing E, and then these two discursive processes loom the looming of the embedding discursive process, where counter-information w loomed in the counter-discursive process looms embedding (£ in one or another way and embedding ® looms embedding information e in one or another way. In fact, four processes in the third line of LCSs constitute the beginning of the process of 22 discursive embedding S^. This process can be- understood to be completely parallel, thus, it can be adequately expressed in the form PCE8. (((« «) 11= (a 11= CC; (E 4 a; E IN w; w C) ) |f= (w e i w; e 11= 8; e =|| O) The last formula, which was logically deduced from L®e by universalizing operators L and J by operators and m, can be read in the following way. embedding discourse is constituted by counter-discourse which parallel Informs the four characteristic parallel processes of embedding of counter-information w, concerning informational embedding ® and embedding information e (as shown by the third line of PiSe). In short, PEe can be rewritten into = |(= (« (E; E 4 w; e IM; e ) where = lt= 11= C m «; C \p w; w =11 (£) ) ; S^ H (a N a) It could be said that the last three expressions are in accordance with the equivalence system Da. However, formula P£e does not say how or where the counter-discourse 8 will be embedded co by means of embedding discourse 8^. This answer will be given in the next section. 3.4. The Game of Informing, Counter-informing, and Informational Embedding within a Discourse of an Informational Entity information w, looms into source information a in one or another way and, thus, informationally impacts the basic process of discourse « |= a. To remain consequent in the relation of possibility of decomposition, the basic process a t= a could be replaced by the cyclic system a 1= 3; 3 =( a; 3 ^ a; a =^ 3 or in the case of looming by a L 3; 3 J a; 3 L a; a J 3 Probably, the last interpretation can satisfy the taste of a theorist's view for it does not limit in any respect the possibility of further development of formal treating of informational phenomenology in question. The next step in the cyclic game of discourse is the well-known transition from the process of looming into the process of parallel informing. Thus, LDa becomes PDa. (((« N «) 1^= (a IN (Z a; C ||= w; w =i| C) ) L (w C; ® =^1 w; e e; e =« C)) L (e IN a; a e; « }= cc) This formula images the self-discursive game within informational entity a. In this formula, entity e functions as the resulting backward information concerning the discourse within an informational entity o. Through closing of the discursive cycle, partial discursive components ^a' ^w' ^e' previously as non- cyclic components, can get a new, dynamic meaning. And this is the case explicated in PDa in respect to DCw. It is believed that according to the previous discussion the reader could be capable to develop autonomously any connective information (or formal proving) if necessary. The course of discourse within an informational entity depends essentially from the game in which informing, counter-informing, and informational embedding take part as substantial informational players. This game is circular in the sense that after the looming of discourse 8^, this is closed via counter- discourse 8^ and embedding discourse 8^ into the so-called discursive cycle. This cycle was already described by formula DCw in the previous section. The game of discursive looming as the beginning of the game of discourse can be described according to LCCw and L®£ and considering Daw by 4. DISCOURSE AS INTERINFORMATIONAL INFORMING ... Pragmatic mathematics (which in fact is everyday, standard mathematics) plunges through its applying into experimental sciences and, in the last consequence, through them can be experimentally proven or disproven. Zvonimir Sikić [2] 32 4.1. General Informing within a Discourse among Several Informational Entities LDa. (({a a) L (a L E; E J «; (E L w; w J £)) L (w L CE; e J w; e L e; e J O) L (£La;aJ£;a(=a) This formula is cyclic within the basic process a t= a. The last line of the formula can be read in the following way: embedding information e, which carries information on arisen counter- The discourse between two entities (for Instance, existent things, individuals, informational items, etc.) has to be understood always as composed of two types of processes: the inter-entities' and the self-entity's one. It means that each entity discursively involved performs the interinformational and self-informational informing simultaneously. Thus, formulas of self-informational informing within a discourse remain valid also within an interinformational discursive process. What in fact is a discourse between two informational entities? It is a kind of communication in which entities communicate with themselves and each of them with the other one. If so, it is necessary to study the basic discursive process postulating Bl. a, P a, ß in detail, considering that a as well as ß is "speaking" as well as "addressed" component simultaneously. To study processes in detail, within informational logic, means to develop more and more detailed formulas and join them to the initial informational system. A further generalization of the discourse can be studied starting by the discursive formula B2. a, ß, , T a, ß. where particular discursive processes among entities a, ß, ... , f take place. Formula B2 enables the two-way discourse among all Informational entities (a, ß, ... , f ) » occurring on the left and on the right side of the formula. It is worth mentioning that the one-way discourse between entities a and ß is possible, denoting this initially by B3. a ^ ß In this case a remains always the transmitter and ß always the receptor of a's messages. In this relation, a and ß remain discursive within themselves, but only ot transmits information to ß while ß remains against a a pure informational receptor. In the two-way process a, ß ^ a, ß, transmitting and receiving roles of « and ß are interchanging, so, both of them can function as the transmitter and receptor. A more general one-way discourse can be expressed by the formula B4. a. T N T)- where entities a, ß, ... , Y. ?< 11/ ••• » K mark the pairwise different entities and where entities a, ß, ... , f function as transmitters and t), ... , as receptors. The so-called self-discursiveness of an informational entity a was logically postulated by DNa through the scheme (a f:) V ([= a). But, this formula does not concern merely the self-discursiveness, for it is an open formula (by the use of unary operators [=, which are always open to the other side) and thus can communicate not only to itself, but also to any other informational entity. In fact, a |= is to be understood as the formula B5. a t= a, ß. which on the right side of ^ is not limited by distinct informational entities, postulating B6. (a N) (a t= a, ß.....T) Similarly, t= a is to be understood as B7. a, ß, ... , Y N « B8. (N «) (a, , Y t= «) Formulas B6 and B8 can be expressed in a general form, if it is said that a informs and/or is informed discursively in one or another way. In this case, 06 and B8 become B9. ((«[=) V (=i «)) ((a a, ß, ... , Y) V (a, ß, ... , Y =i a)) BIO. ((h a) V (« ^^ ((a, ß, ... , Y N a) V (a =i «- ß. • • • - T)) respectively. 4.2. Counter-informing within a Discourse among Several Informational Entitles In this section the following basic forms of discursive informing will be examined: Bll. a ß, a, ß, ... , Y N a, PN«, P. and a, ß, ... , Y t= a. The first two cases denote the so-called oneway informing and the last two cases the two-way one. According to these cases, the following notations of appéaring discursive components can be introduced: B12. 5(a), S(a, w), and 6(a, e) These entities mark a's discursive components as described by Da, within which lE(a), w(a), (Sla}, and e (a) appear as counter-informing, counter-information, informational embedding, and embedding information, respectively. Further, a marks any operand-informational entity in the upper cases, so, a 6 t«, ß, ... , Y- T), ... , j;} According to Da, the following self-discursive equivalences, called o's self-discourse, counter-discourse, and embedding discourse, marked by B13. 5(a) = (a 1= a); 5(a, w) = (6(a) |= Ci;(a)) (= (o(a); 5(a, e) = (5(a, w) [= C(a) ) |= e(a) can be introduced, respectively, for a £ {a, ß, ■•• < Yi 5/ 11» ■•• , Together with these equivalences, the following inter-discursive cases, called (a [= ß)'s discourse, counter-discourse, and embedding discourse, marked by B14. 5(a ß) = (a ß); 5(a ß; w) = (8(a |= ß ) N (i:(a h ß)) \= w(a t= ß); 5(a 1= ß; E) = (S(a t= ß; w) 1= e(a \= ß)) |= e(a 1= ß) can be introduced, respectively, for pairwise different ct and ß, where a, ß G [ex, ß, ... ,7, 7), ... , Of course, it can happen that some of these particular discourses do not appear or, as it is said, are void. As we see, B14 is only a particular case of B13, if a in B13 marks any informational entity. 4.2.1. The Counter-discursive Case a ß Informational process, marked by a ^ ß, has its own, characteristically (one-way) shaped counter-discursiveness. The initial question is; how does the phenomenon of counter-discourse within cx ^ ß begin? At the beginning, there is the looming (or bursting) of all possible forms of counter-informing processes E(c<), C!;(ß), and E(a ß) and corresponding counter-informational products oj(a), w(ß), and co(a ^ ß), produced by count e r-in f orming processes in one or another way. Similarly to LCco there is B15. (a t= ß) L (cc L Kcc); E(a) J a; (£(«) L w(a); co(a) J (£(«); ß L E(ß); Ci;(ß) J ß; (5:(ß) L w(ß); co(ß) J Q;(ß); ( t= T), <1. e {a, ß.....-r), T e T)..... anđ the corresponding counter-informational products B18. w(q>), qp 6 (a, ß, ... , T, n. ••■ . 2:1; w(

; CE(); W(9M1C(9))); (3(4^ € {a, ß, ... , Yl, T e T), ... , ((4; 1) Ih 1= T); (£(4^ 1= T) =11 (4- N t); (£(4, 1= T) Ih w(4^ 1= T); w(4' 1= T) 4 5(4' N T»))) It could be said that formula B19 is universalized by replacing L by |h and J by getting the equivalent part of B20 or that the equivalent part of B20 is particularized by replacing |h by L or 4 by J, getting BX9. In B20, 8^(a, ß, ... , Y 1= T), ... , w) marks the adequate counter-discourse which continues into discursive embedding. 4.2.2. The Counter-discursive case «, ß, • • • , Y N 5/ T), ... , ? This case represents the most general, inductively broadened one-way discourse among informational transmitters «, ß, ... , Y ^^d receptors t), ... , Thus, the discussion from section 4.2.1 can be repeated in a general way. At the beginning, there is the looming (or bursting) of all possible forms of counter- 4.2.3. The Counter-discursive Case a, ß «, ß In this case, counter-discursive informing takes part between both discursive partners, so that the transmitting and receiving roles of a and ß change during the discursive process. It is simply said that between o and ß a two-way discourse exists. At the beginning, there is the looming (or bursting) of all possible forms of counter-informing processes (j;(a), C{ß), )))) This formula includes four counter-informational processes for each informational entity a, ß, ... , Y C^" fact, self-discursive counter-informational components) and for each interdiscursive process 9^4», where 9 ^ variables 9 and fly over entities a, ß, ... , Y- Thus, this formula describes the beginning of the arising of counter-discourses 6(a, w), 6(ß, w), ... , S(y, w) and 6(9 ^ 4^; w), where again 9 # 4^ and variables 9 and 4^ fly over entities a, ß, ... , Y/ out of .discourse 5(a, ß, ... , y h «/ ß- •■• . y). After the occurrence of looming, the looming processes of counter-informing pass over to their regular parallel forms, thus, to the resulting counter-discourse 5j.(a, ß, . . . , Y 1= a, ß, ... , Y; V) within ot, ß, ... , Y 1= a, ß, ... ,7 = B26. Sj.(a, ß, ... , Y N a, ß, ... , y; w) = ((a, ß, . . . , y N «. ß. ■ • . . y) L. (((3(9 e [a, ß, ... , Yl). (9 11= C(9); (j:(9) =11 ))); (3((9, 4- e {«, ß, ... , y}) A (9 4^)). ((9 4,) 11= £(9 4;); £(9 4;) =j| {9 |= 4^) ; 1(9 1= 4^) 11= w(9 4-); u(9 4^) 4 <£(9 1= 4-))))) This formu\a completes the discussion concerning the resultant counter-discursive component Sj.(a, ß, . . . , y h ß, . . . , Y; w) belonging to the two-way informational process a, ß, ... , Y a, ß, .. . , Y. In this case it is assumed that informational entities a, ß, ... , y participate equally and mutually in the process of discourse. It can be simply said that among a, ß, ... , Y ^ two-way discourse exists. At the beginning, there is the looming (or bursting) of all possible forms of counter-informing processes B23. (j;(a), E(ß).....(£(7) and ö;(9 t= 4^); 9. 4' G fot/ ß. ... , Y) and the corresponding counter-informational products B24. w(a), w(ß), ... , (o(Y) and w(9 [= 4'); tp. 4» e {a, ß, ... , y) produced by counter-informing processes in one or another way. Similarly to B21 there is 4.3. Informational Embedding within a Discourse among Several Informational Entities We have to determine four resulting embedding discourses, namely, B27. S^(a|=ß;£), Sr(a, ß, ... , Y T), ... , 8), 5j.(a, ß f= a, ß; 8), and Sj-Ca, ß, ... , Y a, ßf ••. , Y; e) The first two cases belong to one-way discourse and the second two cases to two-way discourse. As any information, also these discursive components first loom and then inform out of counter-informational discursive components, thus, having their looming and then their parallel informing phases. This embedding phenomenology becomes similar to the previous, counter-informational one. 4.3.1. Embedding Discourse within the One-way Process « t= ß The looming of informational embedding CS and embedding information e proceeds out of arisen counter-information w. Methodologically, in the case of a f= ß, there is S(a [= ß; co) ^ S(a t= ß; e). As counter-informational discourse, embedding discourse is only a part within the cyclic discursive process of a ß. It is possible to construct the following looming process; B28. Sj.(a N ß; w) L (w(a) L e(a); e(a) J lo(cx); (£(a) L e(a); e(«) J £(«); w(ß) L ffi(ß); C£(ß) J co(ß); e(ß) L £(ß); e(ß) J Cg(ß); w(a (= ß) L (g(a 1= ß); ®{« t= ß) J w{« t= ß ) ; £(« t= ß) L £(« t= ß); e(a t= ß) J C£(a ß)) The embedding discourse for the case a ß after looming is the following B29. 5j.(a h ß; e) s (Sj.(a h ß; w) IN (w(a) 11= £(«); ®(«) =11 co(«); E(a) |}= £(«); £(a) E(a); W(ß) e(ß); e(ß) 4 w(ß); e(ß) ||= e(ß); e(ß) 4 E(ß); w(a 1= ß) |!= ®(a t= ß); Cg(a ß) 4 w(a |= ß); £(« N ß) IN £(a 1= ß); £(« \= ß) =11 e(a |= ß))) This formula completes the discussion on oneway embedding discourse of the case a ß• 4.3.2. Embedding Discourse within the One-way Process a, ß, ... , T |= T), ... , ? At the beginning of this one-way case of embedding discourse there is the usual looming process ; B30. ß.....r 1= 11.....CO) L ((3(

N T) =11 w(4' T); (£(4. t= T) 11= £(4» (= T); £( This formula includes four Informationally embedding processes for each entity a, ß, a ß, and ß ^ a, respectively, and describes the beginning of the arising of embedding discourses 5(a, e), 5(ß, s), 6(a N= ßf 1 S(ß a; £) out of discourse S(a, ß a, ß; y). After the occurrence of looming, the looming processes of embedding pass over to their regular parallel forms, thus, to the resulting discourse of embedding S (a, ß a, ß ; £) within a, ß a, ß: B33. 8j.(a, ß 1= «, ß; e) = (Sj.(a, ß t= a, ß; w) IN (w{a) IN e(a); (£(«) 4 u(«); lS(a) |N e (a); . £(a) =i| (g(a); w(ß) 11= e(ß); (g(ß) =11 w(ß); (g(ß) 11= £(ß); E(ß) i ffi(ß); (o(ot \= ß) |t= (g(a 1= ß); (E(a ^ ß) ^ ß); (£(« 1= ß) £(« ß); e(a ^ ß) =i| (E(a )= ß); w(ß h a) IN (£(ß h «); Ce(ß |= a) Hl w(ß N «); ®(ß 1= a) |t= e(ß a); e(ß != a) =|1 C5(ß «))) So far, this formula completes the discussion concerning the resultant embedding component Sj.(a, ß ^ a, ß; e) belonging to the process a, ß N a, ß. 4.3.4. Embedding Discourse within the Two-way Process a, ß, ... , Y t= a, ß, ... , Y In this case it is assumed that informational entities a, ß, ... , y participate equally and mutually in the embedding part of discourse. It can be simply said that among a, ß, ... , Y a two-way embedding discourse exists. At the beginning, there is the looming (or bursting) of all possible forms of informat ionally embedding processes B34. ®(cp 1= 4;); 9, cj; e {a, ß, ... where l£(

t= 4^); K; 0(, ß t= a, ß; or a, ß, ... , T 1= a, ß, ... , T We see how a looms the entire, cyclic discursive process within Itself, since at the end of the last formula the embedding information e(a) looms back into a. After looming, formula B38 describes a regular discursive process within a, where discursive components appearing in B38 are the following: B40. S^(a) = (« N «); 5j.(a, u) = (a 1= E(ot); (£(«) a; CS;(a) (= w(a); w(a) =i E{oc)); 8j.(«, E) = (w{a) [= (g(«); £(«) ^ a){a); e(a) \= e(a); t{a) =| e{a)); Sj^(a) = (e(a) |= a; a =| e(a)) The first and the fourth equivalence are in no way in contradiction, since, by definition, e(a) is an internal affair of a. Thus, also B41. = (a, E 1= a; a =1 ot, e ) reflects the known phenomenology of an arbitrary informational entity a. By this kind of discussion, phenomena of the discursive nature of information, considering specific discursive components, are believed to be sufficiently clarified. 5. LACANIAK FORMS OF DISCOURSE . . . The false as well as true science can be put into formulas. Jacques Lacan [9] 17 5.1. A General Scenario of Lacanian Discourse . . . Nature provides us with, let us speak out also this word, markers and these markers organize in an inaugural manner human relations, give them structures and model them. Jacques Lacan [9] 26 The ideas of treating the so-called Lacanian discourse in the way of informational logic have been mainly seized from Bracher [7]. Later, in the course of informational analysis, it could be demonstrated that the apparatus of informational logic enables analysis, which might go behind. the Lacanian ideas, more and more into informational details, bringing to the surface constructive capabilities of the Lacanian concept of discourse. A discourse as informational process (in brain, within interaction of the living) produces informational effects in psychical economies of relative informational transmitter a and relative infonaational receptor ß, i.e. in the metaphysical or informationally total domain of a and ß. In general, both « and ß can be understood as autopoietical informational phenomenon being involved or mutually and individually impacted by the process of discourse. It is possible to imagine how a two-way discursive process, symbolically expressed l^y <*/ ß t= <*i ßi changes the social behavior and how it is Informationally thrown into the domain of wish rather than into the domain of knowledge. This conclusion might not be important on the general level of discussion, however, can become relevant at the detailed analysis of discursive phenomenology of information. It is possible to think that information, which informs, interpellates information which is addressed by informing and that this informational interpellation is a specific or particular function or operation marked by the discursive metaoperator occurring between impacting and impacted informational entitles « and ß. The two-way communicational process marked by a, ß ^ a, ß performs (or informs) a specific (or particular) type of information (or informational arising), within which the relative roles of transmitters and receptors are exchanged during the flow of discourse. According to Lacan, it is possible to study (or introduce) four basic entities, called performing (acting, behaving), truth. Other and production and mark them symbolically by d, x, p, and X, respectively. Further, it is possible to decompose the circumstantial (relative) transmitter a into a self-discursive process of the form (i)^ (= t^) j= (p^ |= or specifically (Lacanianly) into the form (d^ / t^) |= (p^ / X^); similarly, the circumstantial (relative) receptor ß can be decomposed into ^ -Cß) ^ (pp [= Xß) or specifically (Lacanianly) into the form (^p / Tß) N (Pß / Xß); further, the discursive process between transmitter a and receptor ß, i.e. a ß, can be decomposed into (<>„ 1= 1= fPß N specifically (Lacanianly) into the form (d^ / -c^) [= (p^ / Xp); finally, the discursive process between receptor ß and transmitter a, i.e. ß |= tx, can be decomposed into the interdiscursive process of the form (d^ \= t^ ) [= ( p^ X^) or specifically (Lacanianly) into the form (dp / Tg) (p^ / X^). In these expressions, "/" and are particular (Lacanian) informational operators. The general form of these processes occurring within circumstantial (relative) transmitter a, circumstantial (relative) receptor ß, and between circumstantial (relative) transmitter a and circumstantial (relative) receptor ß, and vice versa, can be decomposed as LI. («, ß f= a, ß) N Tp) N (P«t= (Pp Xp)) or specifically (Lacanianly) L2. (a, ß a, ß) (P„ / (Pp / Xp)) L3". (0 / T) ^ (p / X) / Tp) It is worth to mention the following important facts to these formulas: formula a, ß [= a, ß in LI and L2 ensures all possible cases of self and mutual discourse concerning relative transmitter a and relative receptor ß, i.e. the processes at=a, ßt=cc, and ß ß. Further, operators and / appearing in LI and L2 can be particularized to some general degree, for instance, in the case of L2 into L2'. (a, ß t= ot, ß) 1= ^^p /ß -ß) ^ (P«/«^«)' , ß performs as a steady receptor, which does not interact backwards to the transmitter a. Further, operator |= was particularized by operator |N, which explicates the parallel processing between transmitter « and receptor ß and inside of them. It is also to understand that / t^ and dp / Tß are the so-called speaking parts, and p^ / X^ and p^ / X^ are the listening parts of transmitter and receptor, respectively. The next question which has to be touched is how can the impacting of receptor on transmitter be brought into consideration. In a real discourse, a two-way interaction comes always into existence, thus the following Lacanian discursive system can be appropriated: JL<-». «, ß (= a, ß; LTx<-^. a, ß IN / T^), (^p / LRx«-». (p„ / IN a; « IN IN T^) IN IN (C^a IN-«) IN^«) IN T^; ß, a IN (Pß / Xß), (P« / X^); ' ^ß) 1^= (Pß / (P« / X«); ß IN i^ß ; (Pß / Xß) IN ß; ((^ß IN Tß) IN TTp) dp; ((Tß IN "ß) IN ^ß) IN Tß This system is formally syitmietric in regard to the transmitter a and receptor ß. It is in no way closed', so it can be always developed (progressively decomposed) to the needed details by adding new formulas and decomposing the appearing operands and operators, and also particularizing and universalizing them. We can see how initial Lacanian idea of discourse becomes more and more formally complex and that this complexity grows with the number of participants in the discourse. In this way it is possible to show a sufficiently clean Lacanian discursive system of several participants in which each participant is performing harmonically as transmitter and receiver. This completely symmetric system of several participants in a discourse has the form: L«-». La«-^. Lß*^. «, ß, ... , y IN «/ ß, • • • , y; a IN / T^), (^ß / Tß). (^a I (Pcx I (Pß / ^ßJ- ••■ , (P^ / X^); (P« / X^) IN « IN IN"«) INO«; {{T« IN K^) IN IN T^; « IN (P« / x^), (Pß / Xß), • • • / (Py / X.^); ß IN (0« / T^), (Oß / Tß), •■• , / T.^); (Oß / Tß) IN (P« / x^), (Pß / Xß), ••• , (P^ / x.^); (pß/Xp)|Nß; ß IN Ttß; (tOß IN Tß) IN TTß) IN Oß; ((-Tß IN Uß) IN Oß) IN Tß ß IN (p« / x^), (Pß / Xß), • ■ • , (p:^ / x.^) ; ly«-»- y in (0« / T^), (oß / Tß), ••• , / t^); / T^) IN (p« / X^), (Pß / Xß), (0« / T^) IN (P« / xj, (Pß / Xß); (p^ / x^) IN y; • • • , (P.^ / X^); T lt= ^yi 11= T^) IN t^) IM^; ' ((-r^ IN t^) IN -a^) IN T^ r IN (P„ / (Pp / Xß), • • • , (p^ / This system can be still particularized, .universalized, and decomposed according to the arising needs and various philosophies and constructions in accordance with the Lacanian (or psychoanalytic) style (or doctrine) of discourse, however also outside of Lacanian (or psychoainaly tic ) concepts. As one can observe, there is a slight conceptual difference between informational systems marked by JI>-» and L<-»; the reader will be able to discover it by himself or herself. 5.2. On the Notion of the Other as Information The notion of the Other concerns counter-information. If one says that there is no the Other of the Other, this would mean that there is no counter-information of counter-information. This seems reasonable because counter-information as phenomenology of information is not yet embedded into the so-called comprehension of existing or source information which produces (generates) counter-information. In this respect, it is not possible to distinguish counter-information from counter-information, although counter-information, if marked as such, is nothing other than information. This discussion merely concerns a part of Lacan's hypothesis hy which he argues that there does not exist the Other of the Other [8, page 50]. By informational terms, the psychoanalytic term the Other is counter-informational on different levels of discourse. And as we have seen, within each simple or composed informational entity, always an inner discourse, the so-called self-discourse occurs. The Other may appear explicitly in the domain of the so-called counter-discourse and implicitly in any other discursive component as a distributed informational phenomenon within information. To which extent the Other will be brought into the "awareness" of information depends exclusively on informational capability concerning discursive embedding, by which parts of counter-discourse can be embedded into existing discourse and other counter-informational parts can be lost (for ever). objectified. Jacques Lacan [9] 26, 27 How can the basic Lacanian scheme of discourse L3 be appropriated? If we take this scheme / T) 1= (p / X) then each element (operand or operator) of it can be occupied (appropriated, informationally substituted) by a particular Lacanian entity. In fact, Lacan chooses a cyclic scheme of four operand elements, namely (T 2 marking the knowledge, denoting the marker-master, 91 marking the object U (plus-de-jouir , also exceeded or remained pleasure), and f denoting the split (castrated) subject. To remember this scheme of operand elements it is convenient to put them into the Lacanian matrix form L8. f so that this matrix can be rotated clockwise, giving four possible matrix types, i.e. L9. ff-, « SI SI a. which will be characteristic for the so-called university, master's, hysteric's, and analyst's discourse, respectively. The question to be cleared concerns the possible meanings of discursive entities cTj^, SI, and $ and their informationally circular impacting. These entities can be understood as informational processes which roughly mark the knowledge (e.g. cognition, belief, faith), marker-master (e.g. truth, ideal, ideology), remnant (Lacanian object, marked by "a"), and split subject (as far as it is constructed as the second in the relation to the marker), respectively. 5.4. On the Meaning of the Psychic Factors f, SI, or^, and tr^. ... On the contrary, every time we speak about the cause, there exists something antinotional, undetermined. 5.3. The Lacan's Idea of the Basic Scheme Appropriation ... - the unconscious is structured as language - ... this is linguistics, which model is an operator game performed within its spontaneity completely by itself -precisely this structure delivers the status of unconscious. It confirms that under the notion of unconscious there exists something which can be marked, attained, and Jacques Lacan [9] 28 It was seen how four kinds of speech can be constructed and understood to mark the main psychical (in fact, metaphysically informational or informationally metaphysical) factors SI, <7^, and <7-2 ■ According to Lacan, these factors can be in the described cyclic relation and each of them is fixed on the position against the other. Let us explain the split subject $ marking the part of information which observes and comprehends (experiences) itself. In this self-comprehension, $ experiences its own sense and identity, however, observes also its disaffection to itself (counter-information) within the domain of wish. This constitution of $ is the consequence of $'s subordination to categories of symbolic order or language. As a speaking or discursive being, $ identifies itself in and through the language. On the other hand, f feels its own being (informational nature) as unspeakable' or informaticnally connected with that what language to some degree can confirm, but cannot capture it. This informational process is experienced as distress of $'s being. Thus, subject $ is split between the marker-master o-^, which imparts the sense, and remnant SI, which embodies being and cannot be adequately informationally represented (understood). (Tj^ marks the marker-master and represents any marker information to which or against which $ as information is identified. Subject (f invests cr^^ in a way where the marker information functions as the last truth: if (p is confronted with the marker-master it does not feel (inform) anymore a need for additional observation, explanation, or excuse (counter-informing). For the subject the marker-master has a sense, which is self- evident; it is a value existing without the need to be spoken about. According to Lacan, these are the concepts of "ego", "unconscious", and "imagination (fantaey)", used by psychoanalysts. OTj marks the knowledge (or belief), which is the discriminating system of language or of linguistic code and which, according to Lacan, is structured by informational iteration of i.e., by the conquering power, performed by several markers-masters within the discriminating (synchronous) displacement of all other markers. The object 21 has some characteristics of the order of the imaginary and of the real. The remnant marks a part of metaphysics (of a being's total information), a part of autopcietically embodied human being, which is not closed under categories of symbolic order and performs non-symbolically (for instance, signal-informationally or molecular-phenomenologically) too. The remnant marks a disorder which obstructs and indirectly confirms the symbolic and imaginary. As a, remnant, 2J is the cause of wish. According to some Lacanian schemes of discourse [1] it is possible to construct various informational relations (operations) existing within each of four types of Lacanian discourse, since the four psychical factors are also in a specific cyclic relation. Thus, besides the basic relation (■& / t) )= (p / where seems to be a dual (two-way) operator, additionally a general, dynamically structured cyclic scheme of the form LIO. ((((^ p) 1=2 (P / x)) 1=3 x) t=4 -t) t=5 / t) or similar to this form is proposed as a consequence of Lacan's graphic schemes accompanying his philosophy of discourse. In this scheme, and 1=^ can mark a kind of informational incapability or particular non-informing (for instance, within master's and analyst's discourse) and and can mark informational weakness (debility) (for instance, within university and hysteric's discourse). As one can understand, this cycle closes (in an intelligent way) via entities 0 and / T. The last formula is the example how basic Lacanian schemes can be formally decomposed according to Lacan's philosophy, getting more and more detailed "algorithms" for informational treatment of the subject. 5.5. The Phantasm as Information ... Since the unconscious shows us the abyss through which neurosis is reconciled with the real - with the real which could also be undetermined. Jacques Lacan [9] 28 As a consequence of discourse a particular informational form appears and informs during the discourse, which can impact and can be impacted by the governing discursive information (informational kernel) within several types of discourse. This specific informational product will be called phantasm. Phantasm as information playe one of the central roles in Lacanian concept of discourse. Let us proceed from the Lacanian formal expression lll. $ O SJ which marks (an informationally quasi-symmetric) operation or relation between the split subject $ and its object (remnant) ». Tor the mathematically oriented reader it might be not quite clear what do the psychic factors f and 21 in fact represent, however, in the course of psychic (or psychoanalytic) investigation these factors can be always informationally decomposed to the needed or conceptua^ily appropriate detail. As Lacan proposes, object Jt is the sliding or level into which that is embedded, what represents the wish of the subject S. Further, the meaning of operator <> can be determined as 'fantasizes', thus, $ o 21 is read as $ fantasizes 2J. According to the general sense of informational operators, it is even possible to introduce a more general formula of phantasm, i.e., L12. "fß.....'^r^ ^K' \.....\ which can have, for instance, the following meanings: informational entities (split subjects) $ß, ... , fantasize, imagine, wish, etc. informational entitles (their objects, remnants) Sl^i •■• , According to Lacan, it is characteristic that the entities on the left side of operator o are split; it means that these subjects (split informings) perform (inform) as parallel informational entities in themselves. It- is to understand that O is a two-way or quasi-symmetric operation, thus, if the left entity fantasizes the right one, then the right entity also informationally (fantastically) impacts the left one; So, the implication L13. ($ 0 2t) {$, 21 ^ 21) would be appropriate, in general. It is also to understand that 21 stands against This relation is one of the constituents of the psychic economy and is called phantasm. The wish which has to be embedded as information finds its support in phantasm, which is the substrate of the wish, its imaginary regulation. Phantasm appears as a secret, unrevealed informational entity. In fact, phantasm behaves as something informationally ambiguous and paradoxical, for on one side of the phantasmatic operator O there is the last joint of the wish and on the other side something which is informationally embedded into awareness. Thus, phantasm as information belongs to a perverse category, to the domain of absurdity. Phantasm receives its informational function in the unconscious. If it transits to the level of message, a characteristic situation occurs. Phases, within which phantasm transits, belong to the order of pathologic. 5.6. The University Discourse ... The main term, in fact, is not the truth. It is Gewissheit, the certainty. Jacques Lacan [9] 41 which the basic Lacanian discursive scheme (-d / t) (p / X) is appropriated. Thus, let us consider, for example, the four basic informational processes a^a, a(=ß, and ß ß with their informing, counter-informing and embedding and the simplified scheme L3 ' with the aim to obtain the feeling how a more detailed (developed or decomposed) scheme would look like. It is possible to express the adequate cyclic schemes of discourse by means of the so called self-discursive case, for which particular discursive components are determined by B40. Thus, considering the basic positional scheme / t) ^ (p / X), there is: L14. / t(?)) 1= (p(n) / x(n)); (p(T)) / x(r))) =i (^(5) / t(?))); t); co) = / t(?)) n (p(1£(t))) / x((5:(r)))); (p(S;(T5)) / x((r(r)))) =1 (•»(?) / T(^)); i^m^)) / T(C(?))) ^ (p(w(T))) / x{w(r]))); (p(w{T])) / x{w(n))) =1 / t(e(?)))); t= T); O = ((^(w(5)) / t(w(^))) t= (p(e(ri)) / x(ce(iri))); ipm-n)) / x(e(T)))) =1 (-a(w(?)) / t(w(?))); (d(e(?)) / t(c(?))) t= (p(e(r))) / x(e(r7))); (p(e(r))) / x(e(t)))) ^ (d(e(5)) / -r(c(5)))); ((^(e(?)) / T(s(?))) t= (p(Ti) / x(Ti)); (p(t)) / x(r))) h (d(e(?)) / t(e(?)))) for r)) e {ot t= «; « (= ß; ß t= a; ß N ß) The value of cyclic transformation of matrix L8 for the critics of culture lies in the possibility to understand the manipulation of receptors through messages and the transformation of receptors' metaphysics. It is possible to consider the type of interpellation caused by the main four processes of discourse being identified by Lacan. For instance, the university discourse confronts its receptors with the totalitarian system of knowledge or belief (Jby which knowledge is assumed as given. To be able to understand the message, receptors have to be emptied of their own knowledge or belief (t^, thus producing the state of alienation Within the settlement of symbolic order, the receptors do not have any possibility of influence, for and <72 are under the protection of the transmitter (teacher, ideologist). In principle, this is the place from which one begins to learn speech and to which one returns if it tries to comprehend the totalitarian (predominantly ideologically structured) system. Examples of this situation are students in the system of knowledge or belief and socially subordinated individuals in the system of government or bureaucracy. Let us examine the obvious two-way two-subject discourse of the form a, ß a, ß through its mapping onto the scheme of university discourse (Cj / a^) [= (21 / $), by It is to stress that L14 is a rather simplicistic Lacanian system which shows the arising complexity when additional decomposing (detailing) is performed. In the case of university discourse, entities t, p, and X have to be replaced by entities 1X21 SJ/ and respectively. By these replacements in partial discourses of L14, for each partial discourse four subcomponents are obtained, which can be grouped into eight or sixteen processes, respectively, for instance, Sj,(a [= a); Sj.{a t= ß); Sj.(ß f= a); Sj.(ß (= ß) and marked by S^(a, ß), etc. Thus, after the appropriate replacement for the university discourse, there is ; L15. S^««' ß) = ((a2(a) / o-^(a)) f= (2t(a) / f(a)); (21(a) / $(«)) =1 ((72(a) / <7^(a)); (a2(a) / a^(a)) |= (SI(ß} / $(ß)); (2t(ß) / $(ß)) =1 ((r2(a) / a^(a)); (a2(ß) / o-j^(ß)) N (2t(a) / f(a)); (21(a) / $(a)) ^ (a2(ß) / ^^(ß)); ((72{ß) / cr^(ß)) 1= (2t(ß) / $(ß)); (2I(ß) / $(ß)) =1 (<72(ß) / <^i(ß))); 34 Sy(a, ß; w) = (( / cr2(8(ß))) H ((f(w(cx) ((ri(®(ß)) A ($("(«) ( Nonspike columns within bump must have nonzero diagonal elements. Last column within the bump is a spike having a nonzero uppermost element. Typical overall number of spikes is much smaller than the number of columns within the matrix. This is an Important fact which can be exploited for the economical storing of the factorized basis matrix. It is easy to prove that when product form factorization is formed, only those elementary matrices which correspond to spikes'must be actually computed and stored. Other matrices from the product can be replaced by pointers to the non-spike columns (Chvatal, 1983). B with It is easy to check that matrix described structure can be represented as a product of matrices having a following formi Is 0 Fi O Hi where F^ and h' are situated in the same rows and columns as in matrix B. Ig and Ip are unit matrices of dimension s and p respectively. It is assumed that s and p are numbers of column» to the left and to the right of matrix F^, which is of dimension r (s+r+p = m). Therefore B = B^B^. . .sl« < 1 ) Adequate definition for this identity can be "generalized product form of matrix B". B' can be defined as generalized elementary matrices (ordinary elementary matrices, which are contained in product form factorization, can differ from identity matrix only in one column). For matrices structured in such a way the following factorization formula is valid: Is 0 Is C ) Q pi 8 0 pi Hi 'p 0 'p Is C ) 0 Ir (S) "i This identity explains why elementary matrices within particular bump can be computed completely independent from other parts of matr i x . If submatrix F^ is a bump, then factorization (2) is called splitting the bump (Helgason, Kennington, 19B2). Main purpose for its usage is to reduce nurober of nonzero elements in the product form factorization of B. Fill in (creating of new nonzero elements) during the factorization of b' is restricted to r rows which belong to external bump F^. It is an improvement if compared with the usual product form factorization, where creation of new nonzero elements is possible in rows belonging to submatrix H^ as well. Experiences show that this approach saves computer storage in spite of some overhead which is necessary to store additional r elementary matrices (Hellerman, Rarick, 1971, Helgason, Kennington, 1982). Numsrical Phase of the Algoritha Our algorithm for the numerical phase of refactor ization which includes splitting the bump is presented in the continuation. This algorithm is modification of recent algorithm (Helgason, Kennington, 1982) in which we included additional techniques for assuring numerical stability. It was necessary due to the fact that in the mentioned algorithm well scaled matrix was assumed. This assumption is in general quite a realistic one because many mainframe programming packages use some procedures for automatic scaling of data prior to applying the revised simplex algorithm. For example, this is true when MPSX/370 is considered (Benichou et al, 1977). However, such kind of procedure is not included in the PC-LIP. Ue avoided this for the sake of storage economy. The use of scales for rows and columns requires additional storage and, what is more important, practicaly prevents employing of such data structures which take advantage of supersparsity. This is a characteristics of large scale problems which means that the number of distinct numerical values in the problem matrix is usually much smaller than the number of nonzero coefficients (Greenberg, 1976). In the PC-LIP supersparsity is exploited in a standard way: nonzero values within problem matrix are represented by pointers to the table of all distinct nonzero values (Barle, Brad, 1937). Uhen basis matrix is not well scaled, automatically or by means of proper problem formulation, preassigned pivot can appear to be too small and for this reason inadequate. Two cases, which must be treated differently are: I. Inadequate pivot is situated within the external bump. In such a case its corresponding column can be treated in a same way as a spike. This means that such colijmns are included in the process of "spike swapping" (Helgason, Kennington, 1980). In fact this procedure is a variant of partial pivoting which is restricted to spikes within the same bump. 2. Inadequate pivot belongs to column which is outside the bumps (column from the triangle part of the matrix). In this case the only solution is to permute this pivot to the right bottom of the matrix. Such pivots will be referred to as "unstable pivots". In the continuation of the paper we describe our implementation, which includes handling of above cases. Algorithm S CProduct form factorization for a HR matrix including splitting the bump] Preassigned sequence of pivots is represented with vector C, consisting of column indices, and vector R, consisting of row indices. It is assumed that these sequences are the results of Hellerman and Rarick's algorithm. Qthor information obtained with this algorithm can be included into R and C using the following methods indices of spike columns are stored in C with opposite (negative) sign, as well as components of R where external bumps are beginning. Algorithm's input is also basis matrix B, which is of dimension m and parameter TPIVR ("pivot relative tolerance"). All pivots Vp, for which the inequality jy^] < holds, where y^^^ is the largest absolute value of available pivots, are counted as inadequate. Typical values for TPIVR are 0.001 or 0.01. SO: [Divide the pivots into stable and unstable] a) Set (i) n = m for the number of stable pivots (ii) TPIVR = 0.001 (iii) i = 1 b) If i>m, go to SI. c) If Rj <0, go to SO g). d) Set (i ) = R ( i i) . 1 = C^ ym. max |Bki| e) If < TPIVR»y„3^, set (i) for j = i, ..., n-1: fj =■ Rj + 1 = Cj + 1 (ii) Rn = r and C^i = ^ (iii) n = n-1 f) Set i = i+1 and go to SO b> g> Set 1 = Cj (pivot column index) (iii) r = jRj| (pivot row index) (iv> j = 1 (counter for- elementary matrices) b> Alocate storage for (i) y - real vector of dimension m (ii) ETA-file (data structure for storing matrices Ej>-c) Set y = B^^i (1"" column of the matrix B). d> If Ri<0, go to S5. S2: CObtain new lower triangular elementary matr i x3 a) Set z = y. Vector z is the r"^ column of the elementary matrix Ej. b) Set j = j+1. S3s CTest for the last stable pivot3 a) If i=n, go to S16. b) If i0, go to S2. S5: CInitializB for Bump] a) Set (i) d = j (current length of ETA file) (ii) p = i (first column in this external bump) (iii) b = number of columns in this external bump (iv) t = l+b-l (last column in this external bump) b) Set k = p. c) If k>t, go to S6. d) If C|^<0, set k = k+1 and go to S5 c ) e) Set (i) u = Ck ( i i ) v = Ymax = '"^x f> If < set C^ = - C^ g) Set k = k+1 and go to S5 c). S6: CObtain new lower triangular elementary matrixD a) Set fy^ , for k = IRgj (i0, set y = and go to S6. S9: CSpike update] Solve system of linear equations Ed---Ej_iy = SlOi CSwap spikes if |y^| < TPIVR»y„3j,] a) Compute = max for k € CRi,...,Rt> b) If > TPIVR»y„3^, go to S6. c) Obtain new i; for which 1 = jCs| (i0, set i = i-1 and go to S12. b) If C^<0, solve system of equations Ed-'-Ej-lV = B»1 and go to Stl. SI'»: CObtain new lower triangular elementary matrix] a) Set , for k = r y^ , for k = IRg] (s>t) 0 , otherwise Vector 2 is the r*"^ column of the elementary matrix Ej. b) Set j = j+1 S15: CTest for end of bump] a) If i=t, go to S3. b) If i i = i+1 (ii) 1 = |Ci| (iii) r ( iv ) y c) Go to Sl^t. B. '•1 Slài CPartial pivoting] a) If m=n, go to S17. b) Set i = n+1 c) Sort columns having indices from Cj to C^ in such a way that the number of their nonzero elements is increasing, d) In the submatrix containing the rows from Rj to R^ and the columns from C^ to C^ perform Gaussian elimination with partial pivoting. S17: CEndJ Product form of B including splitting the bump is obtained. At the termination of algorithm S, matrix B is represented as a product of elementary matrices B = EiEg.-.E (3> After obtaining this new factorisation of B, its accuracy must be tested. State of the art method for doing this is the so called Aird-Lynch estimate (Rice, 1985). If this estimate shows that (3) is not accurate enough, algorithm S must be repeated with larger value of TPIVR. In our implementation of algorithm S within the PC-LIP, old value of TPIVR is multiplied by 10. Partial pivoting within step SIO c) can be performed by using subroutine BTRAN, which can be restricted to only those elementary matrices which belong to the current bump (Saunders, 1976). BTRAN (Backward TRANsformation) is a historical name for the subroutine which solves systems of the form B^y = d, where B is in a product form. The systems of the form Bz = u, which appear within several steps of the 5 algorithm, can be solved by using subroutine FTRAN (Forward TRANsformation). BTRAN and FTRAN are also important subroutines within the revised simplex algorithm. If row and column permutations determined by R and C are taken into account, all matrices Ej (i=l,2,...,j-1) are either upper triangular or lower triangular, but they are intermixed. That is why (3) is not LU factor ization of B. For this reason the revised simplex algorithm with ordinary product form of basis matrix must be applied after performing the refactorization (as it is in PC-LIP). It is not possible to use those algorithms which use and maintain LU format of the basis matrixj for example Forrest and Tomlin method (Forrest, Tomlin, 1972). If one wishes to use LU format of the basis matrix, splitting the bump can be used only partially on an overall bump or kernel. Kernel is that part of HR matrix which is obtained after the lower and upper triangles have been removed from the matrix. Recently an algorithm was proposed (Helgason, Kennington, 1902) which performs splitting the bump while maintaining the LU format. Ule briefly sketch how our methods for handling the unstable columns can be incorporated in this algorithm. By rearangement of rows and columns, the HR matrix may be placed in the following formi U v W o L T 0 M N L and U are lower and upper triangular matrix respectively, 0 are zero matrices of suitable dimensions. We use T instead of 0 which is used in the mentioned algorithm (Helgason, Kennington, 1992). This enables transfer of nonstable columns to the rightmost part of the matrix. It is easy to check that for matrix B' the following factorization is valid: I 0 O U v u 0 L T ♦ 0 I 0 O M N 0 0 I LU factorization can be performed in usual way for the first matrix at the right hand side. The second matrix is already upper triangular. Due to the fact that a product of two upper triangular matrices is also an upper triangular matrix, LU factorization of B* is obtained. Conclusion« The matrix refactor ization subroutine as described in the paper has been included in the PC-LIP linear programming software package. Our main contribution was that we have combined the already known methods for "splitting the bump" with some methods for assuring numerical stability. The algorithm was tested on many real life problems and proved to be stable even on a very badly scaled data. Algorithm satisfies also with respect to the computational speed. Unfortunately we have not yet had an opportunity for comparising it» performance with some other algorithm performance. It is possible however to measure the amount of reinversion computational time in overall run time. Another interesting test is to examine the effect of inversion frequency on the solution time. We performed these two test on a real life problem with SUS constraints, AS't structural variables and SCtB nonzero elements. With the inversion frequency 20, the optimal solution was obtained after 221 iterations and 565.1 seconds of elapsed time. During the process 12 refactor izations were performed in 1^9.7 seconds. This means that refactorizations amounts to the overall computational time. We used the same problem for the test with the inversion frequency 50. The effect of inversion frequency on solution time: Inver s ion So lut ion I terat ions Time per f requency t i me i teration (iterations) (sees) (sees) 20 ■ 565.1 221 2.55 50 22^» 2.^3 Results show that higher inversion frequency does not effect much the overall solution time. This can be explained with relatively slow execution of the product form variant of revised simplex method. With the use of the Forrest-Tomlin method the performance could be slightly improved (Ashford, Daniel, 1988). References 1. Ashford R.W., R.C. Daniel; " A note on evaluating LP software for personal computers", European Journal of Operations Research,' 35(1988), pp. liO-li^». 2. Benichou M., J.M. Gauthier, G. Hentges, G. Ribiere: "The efficient solution of large-scale linear programming problems - some algorithmic techniques and computational results". Mathematical Programming, 13(1977), pp. 280-322. 3. Chvatal V.: Linear Programming, New York -San Francisco, W.H. Freeman and Company 1983. It. Forrest J.J.H., Tomlin J.A.: "Updated triangular factors of the basis to maintain sparsity in the product form simplex method", Mathematical Programming, 2(1972), pp. 263-278. 5. Greenberg H.J.s "A Tutorial on Matricial Packing", Design and Implementation of Optimization software, Urbino (Italy), (Ed. Greenberg H.J.), Alphen aan den Rijn (Netherlands), Sijthoff and Nordhoff 1978, pp. 109-1^(2. h. Helgason R.V., Kennington J.L.: "Spike swapping in basis reinversion", Naval Research Logistics Quarterly, 27(1980), pp. 697-701. 7. Helgason R.V., Kennington J.L.: "A note on splitting the bump in an elimination factorization", Naval Research Logistics Quarterly, 29(1982), pp. 169-178. 8. Hellerman E., Rarick D.s "Reinversion with the preassigned pivot procedure". Mathematical Programming, 1(1971), pp. 195-216. 9. Rice J.R.: Numerical Methods, Software, and Analysis, New York, McGraw-Hill 1985. 10. Saunders M.A.: "A fast, stable implementation of the simplex method using Bartels-Golub updating". Sparse Matrix Computations, (Eds. Bunch J.R., Rose D.J.), New York, Academic Press 1976, pp. 213-226. 11. Tomlin J.A.! "On scaling linear programming problems". Mathematical Programming Study, ^♦(1975), pp. 1^6-166. 12. Barle J., Grad J.; "PC-LIP: A Microcomputer Linear Programming Package", (program description), Ljubljana, 1987. FORMAL VERIFICATION OF DISTRIBUTED SYSTEMS Keywords: distributed system, model, formal specification, verification Tatjana Kapus, Bogomir Horvat Tehniška fakulteta iVIaribor Distributed systems are inherently concurrent, asynchronous, and nondeterministlc. Formal methods and automated tools are needed for helping in describing them without causing a misinterpretation, and in reasoning about their correctness. Different approaches to modelling, formal specification and verification of distributed systems are discussed uith respect to their abilities. It is difficult to find a universal formal method. Anyway, a formal approach does not have to be universal for being useful in the design of distributed systems. Za porazdeljene sisteme je značilno hkratno in asinhrono izvajanje komponent ter nedeterministično obnašanje. Zato potrebujemo formalne metode in računalniško podprta orodja, ki bi nam pomagala popolno in nedvoumno opisati sisteme ter sklepati o njihovi pravilnosti. V članku govorimo o različnih pristopih k modeliranju, formalni specifikaciji in verifikaciji porazdeljenih sistemov glede na njihove zmožnosti. Težko Je najti univerzalen formalni pristop. Seveda pa je lahko pristop koristen, čeprav ni vsestranski . 0. Introduction Informal software design techniques often rely on trial and error involving possibly several implementation and redesign loops. Formal methods and computer-aided tools are needed in the entire design process to avoid this potentially expensive procedure. This is especially true for distributed systems, because they are inherently concurrent, asynchronous, and nondeterministic. Conceptually, they are thought of as being composed of processes which interact by exchanging messages. If the number of possible interactions is large, their behaviour is extremely difficult to reason informally about, and even to describe without causing a misinterpretation. A variety o verification investigated. computation. different app specification systems by ask abilities. We state explosio and verify saf control and da verified, if a is composition f formal specification and approaches are being They are based on some model of In this paper we discuss roaches to modelling, formal and verification of distributed ing if they have some desirable ask, for example, if they manage n, if it is possible to specify ety and liveness properties, if ta related properties can be proof system based on a model al, which kind of communication can be dealt with, if an approach can be used for different applications, and also, if verification can be easily automated. Note that throughout the paper we talk about the classical system design approach. There, a requirement specification is stated first, which describes the behaviour of a system from its user's view, without talking about its internal structure. It serves as a contract between the user and the designer. A design specification is obtained by decomposing the system into communicating processes. It is the designer's work to verify if it meets the requirement- specification. It is good if every process can be specified separately. The possibility of modular specification and verification of a design against a requirement specification in absence of the code reduces the design complexity of distributed systems. 1. State machines State machines are widely used to model distributed systems. Component processes are represented by states and possible transitions between them. The transitions represent events transmissions and receptions of messages. The system's state space can be obtained, such that its states are determined by a state of every component, and its transitions are the. components' ones. Verification can be generally viewed as requiring reasoning about the complete state space of a system /11/. But, as the number of states increases, it becomes a difficult task. We can say that the basic role of formal techniques is in helping the designer to manage the state explosion. The problem is being solved in two ways. The first one remains in the state-machine concept. After the component processes are formally specified, the sys t em's s t a t e space is constructed and examined. Of course, computers are exploited to do it. This is so-called exhaustive analysis. The state space is in fact a reachability graph, and the analysis is also called reachability analysis. The second .«ay is to use mathematical theories built on appropriate models which would not force us into construction of the state space. culture of an average computer scientist /6/. And formal proofs can play Its role best when a design is clear enough, uhile the designer needs tools for assisting him in the design process to achieve this stage by letting him precisely express his ideas, and in the first place validate them rapidly by simulation. Examples of the tools are OVAL /2/, Veda /6/, RGA /11/, SARA /4/. The tools typically use standardized state-machine languages, such as CClTT's Specification and Description Language (SDL) /2/, and ISO's Estelle /6/, many of them use Petri nets /11/ and related formalisms /4/, for description of systems, because a primary concern here is to provide the designer with a precise and expressive formal language which is easy to learn and to use. This is not the case with abstract mathematical formalisms. One of the problems with exhaustive analysis is that a representation of the complete state space of a system must be constructed. Usually, some transformations have to be performed to obtain a graph of a reasonable size, such as projections, reductions, and selections /11/. They should preserve the behaviour being analyzed. In most cases, transformations are focused on preserving control aspects, and ignoring data aspects of the system. Unfortunately, only some general properties, such as absence of deadlock or livelock, can be proved in this way, or ordering of communication events can be verified. That is why state machines are typically used for verification of communication protocols. Even when projections are used, construction of a reachability graph is time-consuming for large systems. Besides, finite graphs cannot be built sometimes. One solution to the problem, and to make it possible to analyze more system-specific properties, is the use of simulation as a complementary approach. It is in essence exploration of a selected portion of the state space. However, it cannot "prove" properties about the complete state space, but it can increase confidence in the correctness of the system. A much exploited advantage of simulation is that statistical information about the performance of the system may be calculated from the results of a simulated execution. It is said that "exhaustive analysis and simulation are both sides of the same coin" /2/. Some analysis procedures, such as searching for deadlocked states, can be built into a tool. A question arises, how to express specific requirements, to traverse the reachability graph interactively, and to verify if they are met. One way is to write them in the same formalism as the design being verified /14/. The RGA tool /11/ allows the user to specify first-order logic propositions and predicates about places and transitions of its Petri-net designs, and even to write an algorithm to perform more complex analysis of the design. Temporal logic specifications may be written in some tools. There is a similar problem with simula.tlon. In Veda /6/, an observer can be defined to observe execution traces of a simulated system instead of the user, and to report errors when requirement specifications are not met. Another question arises concerning simulation. The development of simulation requires "test scenarios" of the system environment. They can be generated in a fully random or in an interactive way. The authors of SARA /4/, for example, have decided to model the environment explicitly, like the system being designed. A well defined behavioural model of the environment then serves to stimulate the system, and to validate its behaviour. We see that simulation can be in general fully automated. 2. Axiomatic approach Most currently existent computer-aided tools which can be used for design of real scale distributed systems use exhaustive analysis and simulation. One would say that exhaustive analysis and simulation are used because of the lack of appropriate theories. It is true that for many of them only a conceptual framework is provided, mainly concerning communication and concurrency issues, and their use is only shown for small scale problems. Besides, exhaustive analysis and simulation are certainly more easily automated. In the case of finite number of states, algorithmic verification is possible. But there are other reasons. For instance, it is thought that simulation is nearer to the When talking about state-machine notations, we should also mention Mllner's CCS (Calculus of Communicating Systems) /9/, and Hoare's CSP (Communicating Sequential Processes) /5/, although they do not model states explicitly. They rather describe processes in terms of observable events. Their advantage is that they provide a range of algebraic laws for comparing, and reasoning about distributed systems, so that formal specification and verification can be carried out in the same framework. If component processes of a system are described in CCS or CSP, we can still construct the system's "state space". This is indeed convenient for "finite-state" cyclic systems, because the observable behaviour of the system can be obtained and simply compared with the system specification for its correctness. But, to avoid a possibly threatening state explosion, other kinds of reasoning have to be employed with state machines, induction on state transitions, for example. CSP offers besides compositional proof rules. Till nov, we have been talking about constructive descriptions of processes. In the constructive approach, also called operational approach, a process is specified as an abstract machine describing a computation. Such a specification is implementation oriented. We specify a program (i.e. a process) essentially by writing another, presumably simpler, program /7/. For requirement specification and formal verification purposes, specifying processes by stating their properties, constraints that any implementation must satisfy, seems more convenient. This is so-called axiomatic approach. In general, there are two kinds of properties. Safety properties express what may happen, or that something bad must not happen. Examples of them are partial correctness, mutual exclusion, and deadlock-freedom. Liveness properties express what must eventually happen, or that a particular good thing must eventually happen. They are temporal properties. Termination and starvation-freedom are liveness properties. We can talk about the properties in the constructive approach, too. How could we specify a process, if not by describing what may, . or what must happen?! Liveness properties cannot be specified in every model. Only safety properties can be stated and verified within the classical state-machine model. If it is not possible to specify what must happen, the second best way is to express what may happen. The difference between the constructive and the axiomatic approach is that in the former we specify a process executions step by step, and in the latter properties are written in form of logic assertions which hold for execution sequences we would get if the process unfolded over time following the constructive description. Unfortunately, algorithmic verification in the axiomatic approach is not possible in general. Proofs have to be designed by hand (if a theorem prover is not available) and a certain ingenuity often is required to find the proöf /13/. Composi t iona 1 i ty of proof rules means that proof of the correctness of a compound process can be constructed from proofs of correctnes of its parts. Hence, the system's stale space does not need to be constructed. With another word, to prove a property of a program, we do not have to know the complete program, but only requirement specifications of its parts. Hoare has achieved compositionality by introducing a trace model /5/. A trace of the behaviour of a process is a finite sequence of symbols recording the events in which the process has engaged up to some moment in tine. A process in the model satisfies a specification if the specification expression is true for all its possible traces. "Concatenation of sequences", "prefix of a sequence", and "the lenght of a sequence" are basic notations to the trace specifications. A similar approach is used in the compositional proof system for networks of processes of Misra and Chandy /10/. It has to be stressed that safety properties hold for complete execution sequences and their finite prefixes. Some liveness properties are not fulfilled by prefixes, but always hold for complete sequences. Because execution sequences may be infinite, liveness properties are difficult to specify in this model due to flniteness of t races. Temporal logics are most often used for specifying liveness properties. .The temporal operator 'eventually' is especially suitable for expressing progress properties, i.e. that an event will eventually happen. Temporal logic is also used In combination with state-machine model in so-called model checking /13/ for verification of liveness properties. Unfortunately, we need here a finite system state space which we check against temporal logic formulae. Finding models that would allow modular verification of temporal properties, and not only of safety properties, i.e. a compositional proof system for both of them, is a tough problem. An example of such a model is one that has been found by Nguyen et al. /12/. One would expect that infinite sequences will be used in place of finite traces to model process executions. Instead, a behaviour has been introduced for better modelling of progress and termination or deadlock. It is an infinite sequence of observations. Every observation includes a trace of events that have happened up to the moment of the observation. Like in Hoare's traces, the trace may be at most one event longer in the next moment, i.e. in the next observation. It means that events are totally ordered, and that concurrency Is modelled with interleaving of concurrent events. The compositional proof system based on the model uses linear temporal logic /8/. With the introduction of infinite behaviours, i.e. infinite sequences of traces, it has been achieved that the previously mentioned trace notations are still the basic ones, but temporal properties can be stated in terms of them by temporal operators. The model is also Interesting because systems with synchronous and asynchronous communication can be specified and verified, which is not usual in other existent compositional proof systems. Communication is synchronous if a process cannot send anything until the receiving process is ready to accept it as input, and it is asynchronous if a process can send an output as soon as it is ready. To enable modular specification and verification of temporal properties for both kinds of communication, it has been necessary to represent the readiness of processes to communicate in the model. It is not necessary to use temporal logic to express temporal properties. It can be always replaced by first-order, logic with certain relations introduced. The reason it is often used is because it is concise and elegant. Trace specifications are very suitable for data-flov computations, for example, but seem awkward in expressing properties whose data structures are not well-defined sequences, such as properties in unreliable systems. Chen and Yeh /3/ have proposed EBS (Event Based Specification Language) which takes the concept of events more fundamental than that of traces, so that unreliable systems can be more easily specified. Partial ordering on events is used, so that not all possible interleavings of potentially concurrent events have to be considered as with total ordering. And it does not use temporal operators. To say that an event will eventually cause the occurrence of another event, it uses a binary relation. Safety and liveness properties can be specified and verified separately like in Nguyen's system, so that verification is less complex. 3. Conclusion Some approaches to modelling, formal specification and verification of distributed systems have been discussed. We have shown their main characteristics and problems that have to be overcome in searching for new methods. It seems hardly possible to find a universal formal approach. A much exploited solution is in building automated tools which integrate several useful approaches, and do-not force their users into procedures unnatural to them. And perhaps it is true that theories' for specific applications should be established before going into generalization /1/. /6/ Jard, C., Monin, J.-F., and Groz, R. (1988), "Development of Veda, a Prototyping Tool for Distributed Algorithms", IEEE Trans. Software Eng., vol. 14, no. 3, pp. 339-352. /7/ Lamport, L. (1983), "What "good is temporal logic?", Proc. IFIP 83, ed. R.E.A. Mason, North-Holland, pp. 657-668. /8/ Manna, Z., Pnueli, A. (1981), Verification of concurrent programs. Part 1: The temporal framework. Tech. Rep. STAN-CS-81-836, Stanford University, June 1981. /9/ Milner, R. (1980), A Calculus of Communicating Systems, Springer - Verlag, Berlin. /10/ Mlsra, J. and Chandy, K.M. (1981), "Proofs of Networks of Processes", IEEE Trans. Software Eng., vol. SE-7, no. 4, pp. 417-426. /11/ Morgan, E.T. and Razouk. R.R, (1987), "Interactive State-Space Analysis of Concurrent Systems", IEEE Trans. Software Eng., vol. SE-13, no. 10, pp. 1080-1091. /12/ Nguyen, V,, Demèrs, A., Gries, D., Owicki, S. (1986), "A model and temporal proof system for networks of processes". Distributed Computing, vol. 1, no. 1, pp. 7-25. /13/ Pehrson, B. (1989), "Formal Specification Methods", CompEuro 89, Tutorial Sessions, ed. W. Anacker and R. Beyer, Hamburg 1989. /14/ Rea, K, and Johnston, R.de B. (1987), "Automated Analysis of Discrete Communication Behaviour", IEEE Trans. Software Eng., vol. SE-13, no. 10, pp. 1115-1126. References /1/ Boute, R.T. (1988), "On the shortcomings of the axiomatic approach as presently used in computer science", CompEuro 88, System design: Concepts, methods and tools, Brussels 1988, Washington 1988, pp. 184-193. /2/ Cavalli, A.R. and Paul, E. (1988), "Exhaustive analysis and simulation for distributed systems, both sides of the same coin". Distributed Computing, vol. 2, no. 4, pp. 213-225. /3/ Chen, B.-S. and Yeh, R.T. (1983), "Formal Specification and Verification of Distributed Systems", IEEE Trans. Software Eng., vol. SE-9, no. 6, pp. 710-722. /4/ Estrin, G., Fenchel, R.S., Razouk, R.R., and Vernon, M.K. (1986), "SARA (System ARchitects Apprentice): Modelling, Analysis, and Simulation Support for Design of Concurrent Systems", IEEE Trans. Software Eng., vol. SE-12, no. 2, pp. 293-311. /5/ Hoare, C.A.R. (1985), Communicating Sequential Processes, Prentice-Hall International, London. This vork vos stpported ty Research CominitiES of Slownia. CHARACTERIZATION OF CIRCUITS IN GRID OBTAINED BY REGULAR AND SEMI-REGULAR TESSELLATIONS Keywòrds: algorithm, circuit, tessellation Joviša Žunić, Novi Sad Faculty of Engineering Dr Ivan Stojmenović, institute of Mathematics, Novi Sad ABSTRACT: In this paper circuits in grids which are obtained by using plane tessellations are observed. Isomorphism and congruence of circuits in these grids is defined in natural way. Conection between these relations is discussed. 1. INTRODUCTION A tesselation of plane is a covering of the plane by using polygons. It is known that there are exactly eleven ways to cover plane by using regular polygons. Three of these are regular tessellations, where each vertex is surrounded by identical regular polygons (see fig.1}. The other eight are semi-regular tessellations, in which each vertex is surrounded by an identical cycle of regular polygons (see fig.2). C«.3) (3.6) ua) Figure 1. The three regular tesselations (3,3,3,4.0 (3.3,4,3,4) (3.3.3,3.6) (3,4,6,4) (3. 12.12) (4, 6,12) (4.8,8) (3,6,3,6) Figure 2. The eight semi-regular tesselations In this way eleven infinite periodic grids are obtained. (This grids are plane representation of infinite plane graphs.). Let G be one of obtained grids. A circuit of the lenght m in a grid G is a oriented closed path without repeated vertices, containg m edges. A circuit C in the grid G determines a simple polygon which consists of the edges of C. We will say that a circuit C] is congruent'to a circuit C2 iff polygons determined by circuits C^ and Cg are congruent polygons. Also, in natural way we define an isomorphism of circuits in the grid G which is obtained by regular and semi-regular tessellations. Let Ci and Cg be the circuits in the grid G. Then: the circuits Ci and C2 are isomorphic circuits iff there exists a congruence transformation T such that: 1) T maps the grid 6 into itself and 2) T maps a polygon determined by the circuit Ci into polygon determined by circuit C2. Also we say that simple polygons A and B in the grid G are isomorphic polygons iff circuits determined by A and B are isomorphic circuits. 2, WORD REPRESENTATION OF CIRCUITS Let G be one of grids obtained by using tessellations. Grid G is periodic. Let us determine period of grid G. If n is the number of edges in period of G then the number of oriented edges is 2n and we shall denote these oriented edges (vectors) by v(0),v(1),.,.,v(2n-1).la'*'.h1s way for any oriented edge of the grid G there is corrès-^ •ponding-uniquely determined vectcrr"from the set v={v(0), v(1).....v(2n-1)}. Let A. and B be points in the grid G, and P oriented path of lenght t, from A to B, If path P consists of oriented edges v(ii),v(i2)...,,v(it) respectively, then the word f(P)=iiÌ2'-*H which corresponds to path P is uniquely determined. Specialy, for i=1 f(v(i))=i. Let A"^ be the set of all words of lenght k over the alphabet A= ={0,1.....2n-1} and A'=U A"^ k>0. Then denote by A" the set of all words which corresponds to oriented pats in the grid G. That means: aGA'i;=> exists path P such that f(P)=a. If the word a=i the path v(ii)..,v( lenght n determines on the choice of the initial vertex and the orientation of the circuit. A function f maps these 2n oriented paths into 2n words of the set A". Let us denote the set of these 2n words by Q(C) (for circuit C). Let T be isoraetry which maps grid G into itself. Let T(v(i ))=v(i') 1=0,1,2, .,.,2n-1 then (0',1'.....{2n-1)') is permutation of (0,1, ..,,2n-l). Transformation T maps path P=v(i])v{Ì2)... i?...it is from A", then a determines t) such that f(P)=a. The circuit C of 2n closed oriented paths, depending v(it) into path T(P) such that T(P)=T(v(i1)v(Ì2)...v(it)) =T(v(ii))T(v(Ì2))...T(v(it))=v(if)v(Ì2)...v(itJ or f(T(P )=ifi2...it. « HI . I Let A'" Be the set of all words which correspond to circuits in the grid G. Also every word a from A'" (a=i] ...i^) determines circuit C=v(ii)v(i2).. .v(it) (which determines simple polygon with edges of C). Let a and b be words from A'" . We say that a and b are in the relation a iff circuits, which are determined by words a and b, are isomorphic circuits. LEt-IMA 1: Relatione is equivalence relation. PROOF: The set r of all congruence transformations which map grid G into itself is a group. Specialy: If T=I (identical mapping) then for a,bGQ(C)=ö' aab. In the set of vectors {v(0),v(1).....v(2n-1)) we define relation p by: v(i) v(j) <» exists isometry T which maps the grid G into itself such that T(v(i)) = T(v(j)) LEMMA 2: Relation p is a relation of equivalence. PROOF: Directly from definition. Also, we say that: ipj iff v(i)pv(j). ^ If P is a path from point A to point B then vector AB is equal to the vector sum of oriented edges which the path P contains. LEMMA 3: Word a=i ip-.-it ^""O™ ''S ff"'" A'" (or v(it IS circuit) iff 1) v(ii)+v(Ì2)+...+ . -------- . il)v(Ì2)...v. . . , . .. it)=0 (vector summ) and 2) v(ij)+v(ij^,)+...+ v(ij+k)/'0 for kt), representing a circuit iff i^ig ...it is addable. Also it is obvious that a=iiÌ2..,it denotes a circuit iff a(j) satisfied CONDITION-G only for j=l. All words that are a-equivalent to a word a representing a circuit we can obtain using 6,7,8,9 (see input data). We consider only the equivalent words begining by one of initial vectors (input data-5) and sort them in lexicographic order. We choose the first word a' as a representative of this class. Hence, if the word a is equal to a', then word a represents a circuits of lenght t and print it. Our algorithm can be conveniently explained using two phases: extend and reduce. These phases correspond to the addable and nonaddable cases respectively. READ (t) FOR k=l to I DO BEGIN il=Iv(k); m:=1 REPEAT IF iii2..,in, is addable THEN extend ELSE IF iii2...i|n is representative of a nonisomorphic circuits THEM print ilÌ2...im reduce UNTIL m=l END where extends BEGIN m:=m+l; i|n:=c(itn-1.1) END reduces WHILE ip,=c(in,.iC) and mì2 DO m:=m-) IF ra;«1 THEN BEGIN t:=0 REPEAT t:=t+1 UNTIL in,=c(ini-1,t) ira:=c(im-1.t+l) END Data obtained by proposed algorithm will be given in next section, k(t) denoted the number of nortisomorphic circuits lenght of t. Grids which is obtained by tessellations 6',4",3' are not specialy treated, but they have been observed in the papers: |]1,|2|,|3|. The algorithm presented here could be also directly applied to these a rids. 4. CONNECTION BETWEEN ISOMORPHISM AND CONGRUENCE OF CIRCUITS It is clear that if C] and C2 are isomorphic circuits then Cj and C2 are congruent circuits. In this section we will-show that for grfas obtained by tessellnions 3'.4^, 3^4.3.4, 3.4.5.4, 3.5.3.6, 3.12^ 4.6.12, 4.8^ (all semi-regular except 3''.5) is satisfied: if circuits C^ and C2 are congruent circuits then they are isomorphic circuits. For grids obtained by regular tessellations previous statament follows obviously because of that they are not specialy treated. In proofs of following lemmas we will use: LEMMA 6: Let M=MiM2...Mt and N=NiN2...Nt be congruent polygons such that MiiSNii,M,-2=Ni2,Mi2HNi3(for some integres ÌIÌÌ2.Ì3 from (1,2,...,t), then; if points Mii.M^z and are not colinear then Mi=Ni for all iCd ,2,...,t}. We shall denote by ^(i,j) the angle between vecto.rs v(i) and v(j). Qy r(M) will denoted the word m1,2...f..i determined by a simpl polygon M=MiM2...Mt such that mi= » f(Mii^i+l). LEI-IHA 7: Let G be the grid obtained by tessellation 3^4^ then: if M and M are congruent polygons in grid G then r(H)ar(N). PROOF: Equivalence classes with respect to relation p are: I={0,5} II={1,4.9,6} III={2.3.7,81 (see fig.3) Let M=HiM2...Mt and N=N]N2...Nt are congruent polygons in the grid G_and r(M)=ra]m2.. and r(N)=nin2.. .nf Bmymvjxa VECTORS: 5 6 7 8 9.are opposite for: 0 12 3 4 3 4 5 6 12 2 4 "^initial vertex 8 9 10 11 17 32 90 204 f(P) = 0231 208935759020235 7575444084 Mg. J. 1-case:m],n]GI then m^m2.,.mjaOra2...rat and n)n2...n^a0n2 ...nt (words 0m2...m^ and 0n2...n; exist because mi and ni are from same equivalence class) if m2=n2 then by Lemma 6 m{=n{ for i=3,..,,t if mji^ng then we apply reflection in a line determined by vector v(0) which maps grid G into itself. The image of Om^.-.nt is Om^.-.m't. ,0 1 2 3 4 5 6 7 8 9, 0^0 687951324 since ni']=n?, ra^m2...inta0n2... mj-aOnJiDÖ.. .m'j, nin2.. .n^aOn^.. .n^ that means (by Lemma 6J n3=ra3....."t"™! " .rf .rajjon^ng. 2-case: m^n^GHthen n^m2.. .mtolm^. • .nit and nin2.. .ntaln^ ...n; If m2=n2=1 then we continue until but then using Lemma 6 m^=n{ or mira2...m^almg...m^=1n2...njanjn2...n^. 3-case: mi.niSIII then mim2...mta2m2...m^ and nin2..-nta2nó...nl )t2.m|)=H2.n2) if m2=n2 then clearly for i=3,.,.,t and m^nig... mtanin2...nt if m^/n^ then, let be for example, ni2=3 and n2=4, now K3, that means 2m2...mt=236 and 2n2...n{=243 but 2 36a 2 43 4-case: m^G|niSj|then mim2...mtaOra^-•-mt and n^n2... nta0n2...nt )(0,m2)«:^(i ,n2)=^ra2=1 and n2=5 continuing we have Omó... mt=0 154 and 1n2...nt=l 5 4T). but O 1 5 4a 1 5 40 5-case: mjGI, niG|||then m]m2...mjaOm^...m^ and nin2... nta2n2...nf H0,m2)=)(*.n2)='n?=0 and m?G{8,2} if mž=8 applying oq we have mim2...m(.aÖ 2m3...mj nin2...nta20 n2...n( 2 0 n5...nt= we nave mim2.. .mt-au ^ m3.. .mf nino.. .nj-a^ L M0.m3)=.H2.n3)=>inS=0 H2.mä)=n0.n3)'o n continuing we get 0 2m3.. .ra^'O 20 2... am =20 20 ... but this words are not from A'". 6-case: miG|| , niG||| then raim2-• • ■"'t nin2'" nta2n2...nt We are interested in the case when m^ and n^ do not satisfy any of previous observed cases. If for some i one of them is satisfied then we observe polygons Mj.i and .. .N^.^ where Mt+|c=Hk and Nt+k=N|<. Since Hl.m2)=)(2,n2) and m2,n2 do not satisfy cases 1,2,3,4,5 then m2=2 and nž=9. Next, we have Imó...ml'l 29 7 and 2n2...nt=29 7 1 but 1 207 2 9 7 1 therefore niim2... m^an]n2. • -nt- LEMMA 8: Let G be the grid obtained by tessellations 3^.4.3.4. Then: if A and B are congruent polygons then r(A)ar(B). PROOF: Equivalence classes with respect to relation p are: (={0.7.10,17} i|={1,3.6,8,12,14,15,19] ■■■ ={2,4,5,9,11,13,16,18} (see fig.4) si initial vertex f(P) = 13 12 7 15 10 9 13 9 13 16 8 14 19 0 18 11 10 16 11 18 6 0 18 11 5 f VECTORS: 10 11...18 19 are opposite for : 0 1... 8 9 t:' 34567 8 9 10 k(t): 1 2 1 3 6 17 35 101 Fig. 4. Let M=M M2...Mt and N=N^N2...N^ are congruent polygons and r(M =mim2"''''t r(N)=njn2...nt. Case of interest is: case: miG[| , n^G|i| then m^m2...m^alm^...tilt and nin2... nta11n2...nt. Let us observe polygons M'=ABM3...Mt and N =BAN3...n: (see f1g.4a): (r(M")=1ni2...mt and r(N')=11n2...nt)). Since M' and N' are congruent, there exist isometry S which maps plane into itself such that S(M')=S(ABM3...Mt)=S(A)S(B)S^:i3-).. iS(Mt)=BAN3...Nt=N'. But then S is either " - 1) reflection in line s which is symmetry axes of segment |AB|. or 2) half turn with centre in middle of segment |A8|. If S is reflection then images of edges denoted by broken line ( —) do not belong to grid G; therefore ed-Iges of polygon BAN3...N' can be some of edges denoted with ----. Since polygonis conected, we conclude n<7.But for n;7 there are thirteen different a-equivalence classes and representatives of this classes are not congruent polygons so statement follows. In the case when S is half turn, proof is analogous. For grid G obtained by tessellation 3"*.6 (see fig.5) words which correspond to congruence polygons do not have to be a-equivalent. For example: for congruent triangles A and B (as it is shown in fig. 5) r(A)ar(B) but there is no isometry which 1) maps grid G into itself, 2) maps A into B. ^ '■ 28 29 are opposite 13 14 {6 tì 15 VECTORS:15 16 for: 0 1 t: 3 4 5 6 7 8 k{t): 2 2 2 5 5 13 •^-initial vertex f(P) = 23 to 26 22 1 2 22 15 25 9 4 5 26 3 4 5 0 6 27 11 0 6 ^ i-ig. b. The proofs of following lemmas are omited, since they are analogous to proofs of Theorem 1 and Theorem 2. LEMIA 9: Let G be the grid obtained by tesselations 3.4.6.4. Then: if M and N jre congruent polygons in grid G then r(M)ar(N). PROOF: Equivalence classes with respect to relation p are: l={0,1.2,3,4,5,12.13,14,15,16,17) |={6.7,8,9,10,11.18,19.20.21.22,23} VECTORS:12 13 for: 0 1 22 23 are opposite -10 11 t: 3 4 5 6 7 8 9 A 0 k(t): \ oO 3.2 ^ initial vertex f(P) = 1 9 17 16 10 17 16 10 17 23 14 13 7 3 ' 10 17 18 7 3 4 5 22 15 14 13 6 5 0 I ly . U* LEMMA 10: Let G be the grid obtained by tesselation 3.6.3.6, Then: if M and N are polygons in grid G then r(M)ar(N). PROOF: There exist only one equivalence classes with respect to relation p. 1=^(0,i;2;3,4,5,6,7,8,9,10,11} \VECTORS:6 7 8 9 10 11 are opposite for: 0 1 2 3 4 5 V t: k(t): 3 4 5 6 7 8 9 1 J 1 2 1 2 4 initial vertex f(P) = 10 1 2 11 2 O 1 2 3 4 7 6 11 10 6 3 4 79879045098 LEI« 11: Let G be the grid obtained by tessellations 3.12^. Then if M and N are congruent polygons in grid G then r(M)ar(N). PROOF: Equivalence classes with respect to relation p are: l={0,2.4.5,8,10.12,13,14,15,16.17) ■={1.3.5.7,9,11}. VECTORS: 17 7 16 9 12 11 14 13 15 are opposite for : 0 1 2 3 4 5 6 8 10 3 12 13 14 15 15 17 18 1 1 1 3 3 3 1 1 f(P) =1 14 11 0 1 2 3 4 5 15 16 7 8 4 5 15 16 7 8 9 15 14 11 0 ng. o. LEMMA 12-: Let G be the grid obtained by tessellation 4.5.12 then: if M and N are congruent polygons in grid G then r(H)ar(N); PROOF: Equivalence classes with respect to rellation p are: l={0.2.4.5.8.10.18,20.22,24,26.28} ll={ 1.3.5,7.9.11.19,21.23.25.27.29} III ={12,13.14.15.16.17.30.31.32,33,34.35} 0 initial vertex f(P) = 29 28 27 26 25 31 19 18 29 35 6 31 19 18 29 35 23 22 15 9 10 35 23 16 0 1 13 24 23 16 VECTORS: 18 19 ... 34 35 are'opposite for: 0 1 ... 16 17 t: 4 5 6 7 8 9 10 11 12 13 14 15 16 k(t): 1010101030209 Fig. 9. LEMMA 13. Let G be the grid obtained by tessellation 4.82 then: if M. N are congruent polygons in grid G then r(M)ar{N). PROOF: Equivalence classes with respect relation p are: ={0,2,4,6} : ||={1,3,5,7,9,10,11) VECTORS: 4 11 6 8 9 10 are opposite for: 0 12 3 5 7 t: 3 4 5 6 7 8 9 10 11 12 13 14 k(t): 0 1 0 0.0 1 0 1 0 2 0 4 ^ initial vertex f(P) = 28 1 25 10 284967984967 0 3 6 7 0 1 ng. lu. Let grid G be obtained by one of semi-regular tessellations 33.42, 32.4.3.4, 3.4.6.4, 3.6.3.6, 3.122, 4.6.12. 4.82 then from lemmas 6-13 follows: THEOREM 1: Circuits C, and C2 in grid G are isomorphic circuits iff they are congruent circuits. REFERENCES |1| DoroslovaCki R., Stojmenović I., ToSić R., "Generating and counting triangular systems", BIT, 1987, 27. I. 1987, 18-24. |2| Robert A. Metier, "Tessellation graph characterization using Rosettas". Pattern Recogrition Letters 4 (1986) 79-85 |3| Stojmenović I., Tošić R., Doroslovački R., "An algorithm for generating and counting hexagonal systems", Proc. of the 6-th Yugoslav Seminar on Graph -Theory and Lectures for Research Seminar, Dufej-ovnik 1986 , Institut of Mathematics, Univ. of Novi Sad> 1986. 189-198. |4| Tepavčević A., Stojmenović I., "Counting Nonisomorp-hic pats in triangle-hexagonal grids", IX medjunaro-dni simpozij "Kompjuter na sveučilištu". 1987. IISOI. 1-4. |5| ToSić R.. Doroslovački R.. "Characterization of hexagonal systems". Rev. of Res., Fac. of Sci. Math, Ser., Novi Sad 14, 2, 1984, 201-208. |6| 2unić 0., Stojmenović I., "Counting nonisoraorpphic circuits in grids obtained by regular and semi-regular tessellations", XI medjunarodni simpozijum "Kompjuter na sveučilištu", 1989, to appear. ON THE INTERSECTION OF TWO CONVEX POLYGONS Keywords: convex polygon intersection Dragan M. Acketa, Violeta Hauk and Dušan Surla Institute of Mathematics, Nov! Sad Abstract. Given tiro convex polygons P and Q in the plane of size nP and nQ respectively, an 0(nP+nQ) algorithm for determination of their intersection polygon was given in C51. He elaborate the details and special cases of this algorithm (each of the 52 cases is recognized by using three very elementary boolean functions). Thia is incorporated within an implementation in Pascal language. It is shown (what makes a difference from the approach in [5]) that the generation of intersecting points nay be separated from the construction of the intersection polygon itself. O PRESEKU DVA KONVEKSNA POLIGONA. Neka su u ravni data dva konveksna poligona P i Q, sa brojem temena nP i nQ respektivno. U radu [5] je dat algoritam za odredjivanje njihovog presećnog poligona složenosti 0(nP+nQ). U ovom radu su detaljno razradjeni svi mogući slučajevi tog algoritma (svaki od 52 slućaja se prepoznaje pomoću tri jednostavne logičke funkcije), Data je implementacija ovog algoritma u Pascal-u, u kojoj je, za razliku od [5] , ukazano na mogućnost da se generisanje presečnih tačaka razdvoji od konstrukcije samog presečnog poligona. IHTRODUCTIOM A branch of computational geometry is concerned with the problems related to the intersection of given geometric objects. Two problems should be distinguished here : determination and detection of the intersection. Shamos and Hoey have shown in [7] that 0[N ] are necessary to determine the intersection of all pairs of the given N segments. They have given an O(KlogN) algorithm for testing the intersection of two segments and have applied it for testing the intersection of two simple polygons. They have obtained an O(NlogN) algorithm for detection of the intersection of N half-planes and have shown that the simplex method is not optimal. Plane-sweep algorithms for determining the intersection of geometric figures in the plane were considered by Nievergelt and Preparata ([4]). The idea of these algorithms was applied by Hertel et al. ([2]) for determination of the intersection of convex polyhedrons. Mehlhorn and Simos have shown in [3] that the computational complexity of determination of the intersection of polyhedra P and Q, one of which is convex, is of the form 0(n + m + a) « log(n + m + s), where m and n respectively denote the number of edges of P and Q, while s denotes the number of edges of their intersection. Dobkin and Kirkpatrick have developped in [1] a method for testing the intersection of polyhedra with computational complexity Odog N) . Finally, O'Rourke et al. have obtained ([5]) an 0(nP+nQ) algorithm for determining the intersection polygon of convex polygons P and Q with nP and nQ vertices, respectively. This algorithm was also described in the monograph [6], Section 7.2.1. It is this last algorithm that our paper is devoted to. Let P and Q ba two convex polygons in the plane and let P[i], 1<- io nP and Q[j]. 1 <" j<"» nQ respectively be their vertices (ordered w.r.t. the positive orientation, so that the i>olygon surfaces ar« placed on the left w.r.t. the oriented edges). Zn most cases the picture composed oC both polygons is surrounded fay altenatively placed "sickles" between some two neighbouring intersection points. The algorithm from [5] can be follows : sketched as i :- 2; j 2; k 1; REPEAT IK the edges Pti-l]P[i] and Q[j-l]QtJ] intersect THEN record intersection ; ADVAHCE ! (* this procedure call increments either i or j by 1. The main idea is not tc advance on the boundary of the polygon, the current edge of which contains a yet to be found intersection. The procedure AĐVAMCS also includes recording the vertices of P and Q, which should belong to the intersection polygon k k + 1 UNTIL k - 2 • (nP + nQ) ; Roughly, the direction of advancing can be in non-degenerate cases determined by using ttie following two principles: 1) the principle of "forthcoming head advancing" : if one of the two current edges has already crossed over (or at least has reached) the line determined by the other , is front of that other edge, then that other edge, which is forthcoming, should advance. 2) the principle of "right head advancing" : if the principle 1) (which has the priority) cannot be applied, then the edge which should advance lies in the right-hand plane N.r.t to the opposite (oriented) edge. It is guaranteed that two tours around the polygons are sufficient to "catch" all the intersection points. The exit from the REPEAT loop can be declared to be earlier in some cases. The case when no intersection point is recorded is specially treated in [5]. The application of convexity of the polygons is contained in the following observation : one can go around the boundary of a convex polygon (in the positive orientation) by )ceèping left at each vertex (that is, each edge lies in the left hyperplane with respect to the previous oriented edge). This way of moving around the polygons provides an easy possibility to determine which one of the two current edges should be followed when looking for the Intersection points. Our Implementation of the above algorithm can be divided into the following two main steps : STEP 1. Given the arrays P and Q of vertices of input convex polygons, construct the array R of their intersection points. < The main advancing idea is incorporated In this step ) STEP 2. Given the array R of the intersection points, construct the array S of vertices of the intersection polygon. ( This step is a supplement to the basic algorithm ) Remarks. The points in the auxiliary array R are equipped with some additional data, which make the independence performance of the Step 2 possible. The original algorithm in [5] did not use such an auxiliary array, we have introduced it to make the performance of the algorithm more clear. We make the following preparation for the possible second tour around the polygons: FOR 1 := 1 to nP DO P[nP+l] :» Pti]; FOR j := 1 to nQ DO QCnQ+j] := P[3]; We shall use some abbreviations when explaining the advancing mechanism. The endpolnts of the current two edges, P[1-1], PCI], QIj-1] and Q[j] - will be denoted by A,B,C,D respectively. We proceed with the complete Pascal code of pur implementation, excluding some obvious abbreviations. The program is accompanied by appropriate commentaries . PROGRAM PROGRAM Advance; CONST CO ■» 50; (* max.number of points in a polygon *) eps - 0.001; (* tolerance for comparing reals and for testing parallelism *) TYPE realpoint « RECORD x, y : real END; seq = array[l..co] OF realpoint; PQ " 'P'..'Q'; intersectlon_polnt » RECORD point : realpoint; 1, j : Integer; exit : PQ END; interseq = array[1..co] OF lntersectlon_polnt (» Introducing of special data type for recording intersection points Is essential, since it allows an independent performance of Step 2 in our algorithm. If an Intersection point is determined by the edges P[i-1] Ptl] and Q[j-ll Qtj] . then the Indices 1 and j are equal to the corresponding components of the record. The record component exit denotes which one of the polygons P and Q should be followed on the boundary of their Intersection, starting from the current intersection point (the advance step will be always made on the opposite polygon). *) VAR P, Q. S :seq; R :lnterseq; (* two input sequences P and Q, the output sequence S, and the auxiliary sequence R •) nP, nQ, nR, nS, (* the cardinalities of the sequences *) k :Integer; jump :boolean; (* may we jump over the procedure Construet_polygon ? *) {* We start with seven routines needed to distinguish between the cases which decide the actions during advancing : •) FUNCTION Eq( A, B :realpoint) : boolean; (« Are the points A and B approximately equal 7 •) BEGIN Eq := {abs(sqr(A.x - B.x) + sqr(A.y - B.y)) < eps) END; FUNCTION Eqc(a, b :real) : boolean; (* Are the real numbers a and b approximately equal ? ») BEGIN Eqc (abs(a r- b) < eps) END; FUNCTION Coef( A, B: realpoint ): real; (* Coefficient of the line determined by the points A and B *) BEGIN Coef (B.y - A.y)/(B.x - A.x) END; PROCEDURE Line_lntersection ( A. B, C, D ; realpoint; VAR intersection: realpoint ); (» determines the intersection of the lines AB and CD *) BEGIN IF NOT Eqc(A.x, B.x) AND NOT EqcCC.x, D.x) THEN BEGIN (* none of the lines AB and CD is parallel to y-axis *) Intersection.X :•> (Coef(A,B)*A.x - A.y -Coef(C,D)*C.x + C.y) / (Coef(A,B) -Coef(C,D)); intersection.y := Coef(A,B)•(intersection.x-A.x)+A.y; END ELSE (* If AB is "vertical" , but CD is not *) IF Eqc(A.x,B.x> AND NOT Eqe(C.x.D.x) THEN BEGIN intersection.X t« A.x; intersection.y := Coef(C,D) • (intersection.X - D.x)+D.y; END ELSE BEGIN (* if CD is "vertical" ,but AB is not *) intersection.x C.x; Intersection.y := Coef(A,B) • (intersection.x - B.x)+B.y; END; END; (• Llne_lntersection «) FUNCTION ParaK A,B,C,D :realpoint ) :boolean; (* Are the lines AB and CD approximately parallel ? «) VAR par : integer; BEGIN IF NOT Eqc(B.x, A.x) AND NOT Eqc(C.x, D.x) THEN par :» 1; IF Eqc(B.x ,A.x) AND KOT Eqc(D.x ,C.x) THEN par :« 2; IF NOT Eqc(B.X .A.x) AND < Eqc(D.x ,C.x) THEN par :» 3; IF Eqc(B.x ,A.x) AND Eqc(D.x ,C.x) THEN par :•> 4; (* we must avoid comparing some infinite or extremely large coefficients ; this is the reason why we treat separately the cases when at least one of the considered line segments is vertical «) CASE par OF 1: IF NOT Eqc(Coef(A,B), Coef(C,D)) THEN BEGIN Line_intersection ( A, B, C, D, intersection ); Paral := ( abs(intersection.*) > (1/eps) ) OR ( abs(intersection.y) > (1/eps) ) END ELSE Paral := TRUE; 2,3: BEGIN Line_intersection ( A, B, C, D, intersection ); Paral := ( abs(intersection.y) > (1/eps) ) END; 4: Paral TRUE; END (* CASE par *> END; (* Paral *) PROCEDURE Midpoint( F, G, H: realpoint; VAR mid:realpoint ); (» Generates the middle one among three collinear points. The procedure is never applied to non-collinear points *) BEGIN IF F.x <> G.x THEN BEGIN IF (F.x < G.x) AND (G.x < H.x) THEN mid := G; (« analogously FOR the remaining 5 permutations of IF,G,H1 «) ..... END ELSE BEGIN (* the "vertical" case is treated separately *) IF (F.y < G.y) AND (G.y < H.y) THEN mid := G; (*. analogously FOR the remaining 5 permutations of (F,G,H! *) ..... END END; (• Midpoint *) FUNCTION M( F, G, H :realpoint ): boolean; (« TRUE iff G is the middle one among distinct collinear points F, G, H. This function is never applied to non-collinear points •) VAR mid: realpoint; BEGIN M := FALSE; IF (NOT Eq(F,G)) AND (NOT Eq(F,H)) AND (NOT E 0 THEN okay := NOT Eq( Point, R[nR].point ); (« if the current intersection (E) is equal to the previous one (R[nR]), then we should not save it *) IF (nR = 0) OR okay THEN BEGIN nR := nR + 1; R[nR].point := Point; END; (* the three additional components of the record should be always updated, regardless of whether we are actually advancing around the intersection polygon: *) R[nR].i := i mod nP; IF R[nR].i = 0 THEN R[nR].i := nP; RtnR].j := j mod nQ; IF R[nR].j = 0 THEN R[nR].j := nQ; R[nR].exit := Exit; END; (» Record_point *) PROCEDURE Go_on ( Exit: PQ ); (» performs the elementary advancing step in most of the cases when there exists the intersection of the two supporting lines. If the intersection belongs to the both of the current edges, then the procedure writes it down *) BEGIN IF cas IN (36,39,42,45,48,49,50,51,52] (• equivalently, IF both the points defining cas coincide with the intersection E *) THEN Record_point (E, Exit); IF Exit = 'Q' THEN i:= i + 1; IF Exit » THEN j:= j + 1 (* advance along P if the exit Q is recorded and conversely «) END; (» Go_on ») PROCEDURE Treat (Tail, Head, Point: realpoint; Exit: PQ ); (* materializes the principle of "right head advancing" ») BEGIN IF Right (Tail, Head, Point) THEN Go_on (Exit) ELSE Go_on (chr(ord('P')+orđ('Q')-ord(Exit))) (* that is, use the opposite exit ») END; PROCEDURE Write_đown_l ( X:realpoint ); (« records the point X, the exit (as well as the advancing direction) is actually irrelevant, since the next step will have the same outcome in the both possible cases *) BEGIN Record point( X, 'Q'); i:= i+1 END; PROCEDURE Hrite_down_2 ( X, Y:realpoint ); (» similar to the previous procedure, but records two points, X and Y *) BEGIN Record_point( X, 'Q' ) ; Record_point( Y, 'Q' ) ; i:= i+1 END; PROCEDURE Exit_0; (* a pair of edges may be sufficient to decide that the polygon intersection is empty *) BEGIN stop := TRUE; jump := TRUE; writelnC Polygon surfaces of P AND Q are disjoint') END; PROCEDURE Save_exit_l ( X :realpoint ); (* used if it is immediately recognized that X is the only intersection point *) BEGIN stop := TRUE; jump TRUE; nS := 1; 3(1] := X; END; PROCEDURE Save_exit_2 ( X, Y :realpoint ); (* used if it is immediately recognized that X and Y are the only two intersection points •) BEGIN stop := TRUE; jump := TRUE; nS := 2; S[l] := X; S(2] := Y; ENE^ BEGIN (* Intersection_points *) jump ::: FALSE; stop FALSE; i := 2; j := 2; nR := 0; k := 1; (» k = the number of passes through REPEAT ») REPEAT (* the main loop, each pass through it corresponds to one advance step *) IF i = 1 THEN A := P[nP] ELSE A := P[i-1>, IF i>nP THEN i := i MOD nP,- B := P[i]; IF j = 1 THEN C := Q[nQ] ELSE C .:= QEj-l]. IF j>nQ THEN j := j MOD nQ; D := Q[j];' (« The above four IF-statements establisha' connection between the first and the second tour around the input polygons «) (• Recognition of the mutual position of " the current two edges AB and CD ») Extract_case ( A, B, C, D, E, cas ); (» Performing the appropriate action depending on the case involved *) CASE cas OF 3 : Write_down_l( A ) ; 6,10 : Write_down_2( A, B ) ; 4,5,8,9 : Write_down_2( A, D ) ; 20 : Write_down_l( C ) ; 16 : Write_down_2( C, B ) ; 14,15 : Hrite_đown_2( C, D ) ; 1,25 : Exit_0 ; (* disjoint P,Q ») 7 : Save_exit_l( A ) ; 24 : Save_exit_l( B ) ; 21,22 : Save_exit_2( A, B ) ; 11,12,17,18 : Save_exit_2( A, C ) ; 23 : Save_exit_2{ B, D ) ; 13,19 : Save_exit 2( C, D ) ; 27 : IF Right( A,B,C ) AND Right( C,D,A ) THEN Exit_0 ELSE Treat{ A,B,D,'P' ); 32 : Treat( B,B,D,'P' ); 28,30,34,36,37,39.43,45,49 :Treat( E,B,D,'P'); 2,31,33,40,42,44,47,51,52 : i := i + 1; 26,29,35,38,41,46,48,50 : j := j + 1; (* Most of the cases in the last two groups are solved by using the principle of "forthcoming head advancing" *) (* Validity of the above actions is easily checkable by hand. We suggest the reader to draw the small pictures (containing just two oriented edges each), which correspond to each one of the 52 cases *) END; (* CASE cas OF *) IF Eq( R(nR].point , R[l].point) AND ( nR > 1 ) THEN stop := TRUE (* the equality of R(nR].point and R[l].point means that a nontrivial intersection polygon is already completed ») ELSE IF Eq( R(nR].point , R[2].point) AND ( nR > 2 ) THEN (* It may happen that we are unable to stop by recognizing the second appearance of R[l].point. One call of the procedure Write_down_2 records two intersection points ») BEGIN nR := nR - 1; stop := TRUE; END ELSE (* augment the number of passes by 1 *) k := k + 1 UNTIL (k = 2*(nQ+nP)) OR stop; (* All the intersection points (if they exist at all) will be diocovered before the boundaries of the input polygons are passed twice. On the other hand, the construction of the intersection polygon should be terminated at the moment when its boundary becomes closed or when it for some other reason becomes clear that no other intersection points can be found *) IF nR > 1 THEN nR :<= nR - 1 ; (» This is necessary because R[l].point is counted twice •) BHD; (» lntersection_jpoints •) (* The last two procedures are used within the Step 2. of our implementation ») (* The following procedure deals with the cases nR " 0 and nR >• 1. In these eases additional tests are performed in order to check whether the surface of one polygon is completely included into the surface of the other. (Note that similar dileaas are not present whenever nR >°> 3; two intersection points are sufficient for proper initialization of the tour around the intersection polygon), These additional tests do not spoil linearity of the whole algorithm. For instanc«, consider the question whether the whole P is inside Q. It suffices to chec)c whether the point P[l] (or the point P [3] if P[l] coincides with the intersection point) is in the interior of Q. This is true iff PtU (P[2]) lies inside the left half-plane w.r.t. each oriented edge of Q , that is, iff that point is not possibly (placed to the) right fro» (an edge of ) Q *) PROCEDURE Construct_polygon (nP,nQ,nR:integer; P,Q:aeq; R:intorseq; VAR nS:integer;VAR S:seq); (« completes the intersection polygon in the cases when at least two intersection points are present, while no trivial final decision can be made (consequently, the boolean variable "jump" is FALSE) *) VAR start, finish , («the first and the last (inclusively) index of the vertices (of an input polygon) lying on the inner bound of a considered sickle *) w, y -.integer; BEGIN (* appropriate initializations *) nS := 0; R[nR+l]:=R[1]; FOR w:- 1 TO nP DO P[nP+w] :» P[w]; FOR w:- 1 TO nQ DO Q[nQ+w] Q[w]; (» The main FOR-loop; each pass through it corresponds to the completion of such a part of the boundary of the ntersection polygon, which represents the interior boundary of a sickle between the two input polygons «) FOR w:» 1 TO nR DO BEGIN (* Put the intersection point into the intersection polygon ») nS :« nS + 1; S[nS3 :» R[w].point; (• Put the "sickle" points of P or Q, which should lie on the boundary of the intersection polygon between Rtw].point and Rtw+1].point *) IF Rtw].exit - 'P' THEN BEGIN start R[w].i ; finish R[w+ll.i - 1; (* we use the inner indices of the vertices of the inner polygon w.r.t. the sickle ») IF (Rtw].i > R[w+l].i) THEN finish finish + nP; (» the connection between two tours is established *) IF Éq( Rtw].point, Ptstart] ) THEN start :» start + 1; IF Eq( Rtw+1].point, Ptfinish] ) THEN finish finish - 1; (* the last two statements are necessary in order to avoid duplication of the vertices of the intersection polygon in degenerate cases, when an initial polygon vertex coincides with an intersection point *) FOR y start TO finish DO BEGIN nS :« nS + 1; s(nS] Pty] END END; (* IF Rtw].exit =« 'P' «) IF Rtw].exit - 'Q' THEN BEGIN (• Replace i, P, nP in the part under IF Rtw].exit » 'P' by j, Q, nQ respectively and repeat the rest ») ....................END ; END; (« FOR w:- 1 TO nR •) END: (* Construct_polygon *) (* Remark. Although the procedure Construot_polygon includes double-nested FORloops, the required number of steps is not greater than 0(nP + nQ). This follows from the elementary fact that the maximal number cv£ vertices of the intersection polygon is equal to nP + nQ. *) PROCEDURE Hone_or_one( nP, nQ: integer; P, Q: aeq; VAR nS; integer; VAR S: seq; VAR jump: boolean ); (* applies to the cases nR > 0 and nR - 1 *) VAR i,j : integer; pp,qq : realpoint; prfP , prfQ : boolean; (• possibly right from P AND Q respectively *) BEGIN jump :- TRUE; prfP :» FALSE; prfQ :- FALSE; j 1; QtnQ + .1] :- Qtl]; PP PtU ; IF (nR « 1) AND Eq(P tl] .R[1] .point) THEN PP :- Pt2]; REPEAT j j + 1; IF Right( Qtj-1), Q[j], PP ) THEN prfQ :» TRUE xmriL ( j - nQ + 1 ) OR prfQ; i :»> 1; PtnP + 1] :- PHI; qq :- QUI IF (nR - 1) AND Eq(QtlI.RtU-point) THKN qq Qt2]; REPEAT i :» i + 1; IF Right( Pti-1], Pti], qq ) THEN prfP :- TRUE UNTIL { i - nP + 1 ) OR prfP; IF NOT prfQ THEN BEGIN nS :»■ nP; S :» P END (• P is contained within Q ») ELSE IF NOT prfP THEN BEGIN nS :• nQ; S :» Q END (* Q is contained within P *) ELSE (• the i>olygons P and Q are placed outside each other •) IF nR » 0 THEN BEGIN writeln(' Polygon surfaces of P AND Q are disjoint '); nS :- 0 END ELSE (* IF nR -1 *) BKGUI nS :- 1 ; Stl] :- R[l].point END END; {» None_or_one •) BEGIN (» Main program •) (• Input •) read(nP,nQ); FOR k:- 1 TO nP DO BEGIN reađ(Ptkl.X); read(Ptkl.y) END; FOR k:= 1 TO nQ DO BEGIN reađ(Qtk].x); read(Qtk].y) BHD; (• Step 1 ») Interaection_pointfl (nP,nQ,P,Q,nR,nS,R,S,jump) (« Step 2 *) IF nR < 2 THEN None_or_one (nP,nQ,P,Q,nS,S,jump ); IF NOT jump THEN Construct_polygon (nP,nQ,nR,P,Q,R,nS,S)j (* Output ») writeln(' The intersection polygon : '); FOR k:- 1 TO nS DO BEGIN write(Slk].X,• '); writeln(S[k].y) END END. REFERENCES [1] Dobkin, D.P., Kirkpatrick, D.G., Fast detectiop of polyhedral intersection. Theoretical Computer Science 27 (1983), 241-253. [2] Hertel, S., Mantylla, M., Mehlhorn, K., Kievergelt, J., Space sweep solves intersection of convex polyhedra. Acta Informatica 21, 501-519, 1984. [3] Mehlhorn, K., Simon, K., Intersection two polyhedra one of which is convex, [4] Nievergelt, J., Preparata, F.P., Plane-sweep algorithms for intersecting geometric figures. Programming Techniques and Data Structures, Communications of the ACM, Vol. 25, No. 10, 739-747, 1982. [5] O'Rourke, J., Chien, C.B., Olson, T., Naddor, D., A new linear algorithm for intersecting convex polygons. Computer graphics and Image processing, 384-391. [6] Preparata, F.P., Shamos, M.I., Computational geometry, Springer-Verlag, 1985. [7J Shamos, M.I., Hoey, D., Geometric intersection problems, Proc. 17th Annual IEEE Symp. on Foundations of Computer Science, 208-215, 1976. FRAKTALI - ZNANOST ALI UMETNOST INFORMATICA 4/89 Keywords: fractal, iterated function method, Julia set, Mandelbrot set Jasna Đoniagić, Nikola Quid Tehnična fakukteta Maribor V naravi Je veliko objektov In pojavov, kot n.pr. drevesa, gore, oblaki, pretok tekočin, rast populacije, oblika možganskih gub ter podobni pojavi, ki Iz določenega reda preidejo v nered in ki Jih ne moremo matematično predstaviti z običajnimi orodji, lahko pa Jih s fraktalno geometrijo oz. fraktali. V članku obravnavamo naravne in geometrične fraktale, metodo iterativnih funkcijskih sistemov UFS) in nakažemo uporabo formalnih Jezikov. Na koncu izdelamo algoritme za naslednje vrste fraktalov: Juliovo množico, Mandelbrotovo množico in fraktale določene po metodi IFS. ABSTRACT For some natural objects like trees, mountains, clouds, flow of liquids, population growth, surface of brain etc., which turn from order into chaos, it is impossible to describe all mathematical data, but it is possible to present them with fractal geometry or fractals. The purpose of this article is to present natural and geometrical fractals, iterated function method (IFS), and use of the formal languages in the fractal theory. At the end we show some algorithms for creating the following fractals: Julia set, Mandelbrot set, and fractals produced by IFS method. 1. UVOD Beseda fraktal Je latinskega izvora (fractus = zlomljen), torej naj bi spominjala na lomljenje, drobljenje. S fraktalno teorijo se Je pričel ukvarjati Benoit B. Mandelbrot 1980. leta 161, čeprav so matematične osnove za nastanek te teorije ustvarili te mnogo prej P. F. Verhulst, Gaston Julia, Pierre Fatou, Adrien Douady in drugi (71. Fraktale delimo na dve osnovni skupini. In sicer na: naravne in geometrične. Članek obsega opis naravnih in geometričnih fraktalov ter uporabo formalnih Jezikov na področju fraktalne teorije. V povezavi z naravnimi fraktali smo opazovali Verhulstov dinamični proces ter JuUove In Handelbrotove množice. Pri geometričnih fraktalih smo podali metodo IFS in opisali nekatera pravila za generiranje geometričnih fraktalov. Prav tako smo razvili tri algoritme za generiranje fraktalnlh slik. 2. NARAVNI FRAKTALI Naravne fraktale lahko zasledimo na področju geografije, biologije, biokemije in fizike, ko želimo z njimi upodobiti naravne pojave, kot so na primer poplave rek, pretok tekočin, obliko možganskih gub, vaskularni sistem, vreme itn. Ideja za nastanek naravnih fraktalov izvira iz biologije, ko je P. F. Verhulst 1845. leta definiral zakon rasti populacije [71. Zagovarjal je trditev, da lahko določena populacija narašča tako dolgo, dokler ne doseže svojega razsežnostnega maksimuma X. Ce le tega prekorači, velikost populacije pade. Potrebno je bilo več kakor 'sto let, da so dokazali vse nejasnosti te trditve. PriSll so do zanimivih rezultatov : Ce Je faktor rasti majhen, se velikost populacije uravnava sama po sebi in zmeraj ostaja znotraj optimalne vrednosti X. To pomeni, da populacija narašča, kadar je pod optimalno vrednostjo X, in pada, kadar je nad optimalno vrednostjo X. V primeru, da Je faktor rasti velik, taksen, da se populacija poveča za več kakor 200 '/., pa optimalne vrednosti X ni mogoče več doseči. Porodi se vprašanje, ali Je rast populacije sploh kdaj tako velika? Seveda! CloveSke populacije ne naraščajo tako hitro, toda pri nekaterih Insektih tak pojav ni nenavaden. Ugotovili so, da pri 245 '/. povečanju populacije nastanejo oscilacije okoli optimalne vrednosti X z velikostjo periode 2,4,8,16..... dokler pri 257 '/. ne preidemo v zmedo. Kako si razlagamo besedo zmeda? To preprosto pomeni, da delovanja sistema ne moremo več nadzorovati, da je ušla izpod naše kontrole. Najzanimivejša točka Verhulstovega dinamičnega procesa pa ni zmeda sama po sebi, temveč dogodek, ki spremeni red v nered. Verhulst je to trditev matematično dokazal. 2 x označi začetno velikost populacije, z x o n pa velikost populacije po n letih. Jakost rasti populacije R definira relativni prirastek populacije na leto: nestabilnost teh dveh stanj. Pri O ne pride do rasti populacije, saj nimamo s čim začeti. To stanje smatramo za nestabilno, saj že pri 02. Oglejmo si primer, pri katerem postavimo x^= O.1 in r=1.8 (slika 2.1). R = Slika 2.1 Rast populacije pri r=1.8 in 0.1 Nato uvede določene predpostavke: - Populacija lahko naraste do določenega maksimuma X (maksimum normirajmo, tako da Je X=l) - R se naj spreminja glede na velikost populacije in naj bo linearna funkcija od r (r Imenujemo parameter rasti in r>0): R=r(l-x ) n Ob teh predpostavkah dinamični zakon rasti preide v naslednjo obliko: X = f (x n+l n = (l+r)x - rx Vidimo, da velikost populacije x sprva naraSča, saj Je pod maksimalno vrednostjo X=l. V četrtem koraku pride do prekoračitve. Zaradi tega se velikost populacije zmanjša in pade pod 1. To povzroči ponovno rast in takoj za tem ponoven padec itn., dokler se dokončno ne umiri pri stabilni vrednosti X=l. Zanimivejši položaj nastane, kadar je r>2. Zato razisčlmo primer, ko postavimo x^= 0.1 in r=2.3 (slika 2.2) 2.3). ter X = 0.1 in r=2.5 (slika- Ločimo dve stanji, pri katerih populacija ne spreminja velikosti: x = O in x = 1. Zanima nas stabilnost oz. o o vellltofl populacije Slika 2.2 Rast populacije pri r=2.3 in 0. 1 ■ß OJ ? Cj OA t to A E ■'A 1 o o. Ti "(ž) o n "53 > / Slika 2.3 Rast populacije pri r=2.5 in 0.1 Ugotovimo, da pride do periodične oscilacije med nivoji. V prvem primeru dobimo periodo 2, v drugem pa 4. Če bi nadaljevali s postopkom, bi dobili periodo 8,16,32,..., dokler pri r=2.57 ne bi prešli v zmedo in periode ne bi bilo več mogoče doloćltl (slika 2.4). Slika 2.S Verhulstov dlnamltnl proces VpraSall se boste v kakSnl povezavi Je vse to skupaj s fraktali? Verhulstov proces Je enodimenzionalen, Mandelbrot pa Je raziskal popolnoma enak problem, le v 2D prostoru. Odločil se Je opazovati kompleksna števila namesto realnih, pri čemer je sledil procesu x^,. . . , v ravnini, raje kakor na premici. Dejal je, da Imamo v ravnini stekalifeča (attractors), ki se "borijo" za svoj vpliv na ravnini. Točka se v dinamičnem procesu približuje enemu ali drugemu stekaliSču, lahko pa Je na meji (ločnici) med dvema stekallSčema in se ne more opredeliti za enega. Mandelbrotov proces je matematično ekvivalenten Verhulstovem procesu. Izhaja iz preproste formule: X = f(x )= X + C ntl n n pri kateri ločimo dve situaciji: Slika 2.4 Rast populacije pri r=2. 57 In 0.1 V nadaljevanju si lahko zastavimo zanimivo vprašanje: Katero maksimalno vrednost lahko zavzame r, da bi dobili Se' enako stabilno oscilacijo (n.pr. s periodo 2)? Ce Izberemo 2 1. Zaporedje limitira proti neskončnosti In pravimo, da Je neskončnost stekallšče procesa x ■» - |x^| = 1. V tem primeru so števila zaporedja na meji med . dvema stekalIščema. Mejo sestavlja kroZnica enotsf ,ga kroga, ki razdeli ravnino na dve regiji. Nič predstavlja notranje stekallšče, neskončnost pa zunanje stekallšče. b) Ce predvidimo c » O dobimo zaporedje IteraciJ !2 then izberi barvo in goto korak 4 (II) if Stevec_lteraclj = 5000 then izberi barvo O (črno) in goto korak 4 (Iii) if r s 2 and Stevec_lteracij<5000 then goto korak 2 korak 4: Pobarvaj točko (n ,n ) z ustrezno barvo, izberi « y naslednjo točko in pojdi na korak 1. Da bi izboljšali čas računanja, smo upoštevali, da točki (x,y) In (-x,-y) produclrata enak rezultat, saj Je slika simetrična glede na izhodišče. Pozorni moramo biti tudi na izbiro koordinat okna, saj ob njihovi nepravilni izbiri lahko dobimo nezanimivo sliko. Algoritem 2: Handelbrotova množica korak 0: Izberi p , p , q , q min max min max Ap = (p - p )/(a-l) max "^mln Aq (q - q , )/(b-l) max min o, 1. Za vse točke zaslona (n ,n ), n = p q P n = 0,1.....b-1, izvrši naslednje korake. «I korak 1; p„ = p . + n Ap o min p q = q + n Aq Stevec_lteraciJ = O a-1. Pri tretjem algoritmu smo začetno točko izbrali (0,0). Število iteracij Je bilo 32000. Program Je v celoti tekel na PC. Algoritem 3 : metoda IFS korak 0: Okno opazovanja V naj bo velikosti X x Y, pri čemer Je X x Y resolucija zaslona. Okno V razdelimo na L x M kvadratov (označimo Jih z V^j) velikosti doli {L=L/dolž, M=M/dolž). Izberi Stevllo_iteraclJ e L x M. Polje V iniciaiiziraj na O. Izberi začetno točko (x ,y ) 6 R^. o o Stevilo_barv=16. korak 1: for n = O to Stevilo_iteraciJ do begin (• izberi nakjučno transformacijo M^ •) rand = random Število med [0.1]; verjetnost = p^; k = 1; while (verjetnost < rand) do begin k = k+1; verjetnost = verjetnost end; (o izvrši treuisformacijo nad točko •) fx v il=rxyilM L ntl J l „ j k n = lnt(x ); 1 n*l n = int(y . ); (• zaznaj "obisk" v kvadratu V^^ •) V[nJ[n2) + 1; end; korak 2: Poišči maksimalno vrednost max v polju V. Določi barvo pravokotnlka V^^: barva_pravokotnika=barva(V[i 1(J1•15/max) in ga pobarvaj. Slike 6.1, 6.2 in 6.3 so bile izrisane na barvnem brizgainem risalniku Tektronix 4696. korak 2: x - y! y = 2x y + q Povečaj števec_iteraclj. korak 3: Izračunaj r^ = + n n (1) if r>2 then izberi barvo goto korak 4 (ii) if Stevec_lteraciJ=5000 then izberi barvo O (črno) in goto korak 4 (lil) If r s 2 and števec_iteraclj<5000 then goto korak 2 korak 4: Pobarvaj točko (n ) z ustrezno barvo, p q Izberi naslednjo točko in pojdi na korak 1. *ttin= -1.5G UMin= -1.50 Xhajc: 1.50 Unax= 1.50 Slika 6.1 Jullova množica pri c = 0.11031 - 0.670371 pMÌn= -0.74591 qiiin= D. 11196 PMa5<= -0.74448 qiiax= 0.11339 Slika 6.2 Maodelbrotova množica Slika 6.3 Trikotnik Sierplnskega dobljen s pomoCJo metode IFS 7. ZAKLJUČEK Znanost in umetnost sta dva nasprotujoča si načina za izražanje naravnega sveta - prvi analitičen, drug intultativen. S pomoCJo fraktalov smo ti dve poti združili In dokazali, da sta odvisni druga od druge. Fraktall so zanimivi zaradi visoke stopnje vizualne kompleksnosti, čeprav so v svojem bistvu Izredno preprosti. Matematična osnova fraktalne teorije Je enostavna, saj temelji na ponavljanju. Prav zaradi tega Jo Je bilo izredno lahko uporabiti na področju računalništva. Algoritmi za kreiranje fraktalnlh slik potrebujejo malo podatkov, s pomočjo rekurzlje pa so zelo uspešni. Teorija fraktalov Je pomagala zlomiti strogo geometrijo likov. Trendi v svetu pa segajo še dalje. Področje uporabe fraktalov se naglo Siri - od biologije do tekstilne industrije pa vse do drugih, predvsem barvnih grafičnih izdelkov. Možnosti Je torej ogromno -ta članek opisuje le delček njih. 8. LITERATURA 111 M. Barnsley: "Harnesslnj; Chaos for Image Synthesis", Computer Graphics, Volume 22. Number 4, avgust 1988 (2) P.Blanchard: "Complex Analytic Dynamics on the Riemann Sphere", Amer.Hath Soc. 11, 1984, str.85-141 (3) S.Demko: "Construction of Fractal Objects with Iterated Function Systems", Computer Graphics, Volume 19, Number 3, 1985, str.271-278 14] M.Gervautz: "Fractals In Computer Graphics". Proceeding of The Second Austro-Yugoslav Conference on Computer Graphics, str.96-103 (5) J. A.Kaandorp : "Interactive Generation of Fractal Objects", Eurographics'.87, str. 181196 [6] B.B.Mandelbrot: "The Fractal Geometry of Nature", W.H.Freeman, San Francisco, 1982 [71 H.O.Peitgen, P.H.Richter: "The Beauty of Fractals", Springer Verlag, Berlin, Heidelberg. New York, 1986 [8) A.R.Smith: "Plants, Fractals and Formal Languages", Computer Graphics, Volume 18, Number 3, JuliJ 1984, str.1-10 (9) A.TerCelJ: "Fraktali - grafične skrivnosti računalniških umetnikov". Informatica 3/87, str.46-50 PRIMENA METODA INŽENJERSTVA ZNANJA U OBRAZOVANJU Keywords: method, knowledge engineering, artificial intelligence, education Ljubomir Jerinić, Zoran Budimac, Dura Paunić i Mirjana Ivanović u x-adu su opisane metode Inženjerstva znanja kao podoblasti vestačke InteJIgrenclJe, i mogućnosti prlmene tih metoda u obrazovanju. Kao najpogodnija metoda reprezentacije znanja za potrebe obrazovanja Izabran Je sistem okvira Marvina Minskog. Na osnovu takvog pristupa razvijen Je programski sistem OSOF za prikupljanje. Internu reprezentaciju i koriSćenJe znanja u svim vidovima 1 nivoima obrazovanja. 1. UVOD Prema tll, veStaCka inteligencija Je deo računarskih nauka u kojima se projektuJu inteligentni raiunarski sistemi, koji se ponaSaJu na natin slitan inteligenciji u ljudskom ponaSEUiJu, za razumevanje prirodnih Jezika, učenje, rezonovanje, reSavanJe problema i si . VI Je interdisclplinarna nauka 1 potekla Je iz istraživanja Iz domena simboličke obrade podataka i dela psihologije o rasuđivanju. VI istražuje simboličku obradu 1 heurističke procese zaključivanja 1 rezonovanja, kao 1 predstavljanje znanja u obliku pogodnom za zaključivanje uz pomoC raCunara (2). Osnovni pravci istraživanja u okviru VI su: razumevamje prirodnog govora, maSlnsko uCenJe,. automatsko program irsinje, računarska vizija. Inteligentna robotika, in±enJerstvo znanja ltd. Razvojem računarske tehnologije i metoda VI u zadnjih deset godina, približavanjem raCunara svim uzrastima, kao i uvođenjem raCunara u Škole, istraživačima VI obrazovanje postaje interesantno polje rada. Deo VI, Inženjerstvo ananja, po svojoj definiciji, metodama i rezultatima postaje direktno primenljlvo 1 u obrazovanju, sa ciljem krajnje individualizacije obrazovnog procesa. DavnaSnja težnja da Jedan nastavnik ili profesor obrazuje Jednog uCenika ovakvim- pristupom postaje realnost, kao i napredovanje svakog učeni ka prema njegovim sposobnostima. U radu se dalje opisuju metode inženjerstva znanja i njihova primena u obrazovanju. Data Je definicija i klasifikacija načina pretstavlJanja znanja, prihvaćena u Inženjerstvu znainja. IskorlSćena Je metoda M. Minskog 16) za realizaciju univerzalnog programskog paketa OSOF 13J za primenu raCunara u obrazovanj u. 2. INŽENJERSTVO ZUANJA U ranom razdoblju istraživanja u ovoj podoblasti VI, do sredine 70-tlh godina, težilo se Cpod utlcajem psihologije>, iznalaženju op&tih metoda reSavanja problema "ekspertize" znanja, zasnovanih na opStim principima zaključivanja sa psihološkog aspekta. Ovakav pristup se pokazao neefikasnim za Von Neuman-sku oj anizaclji.' raCunara 1 sa m.-ilom primenl JivoSeSu u piaksi. Nedostatak Je prevashodno Sto se unutar opSteg generalizovalo specifično znanje relativno disjunktnlh oblasti. Krajem sedamdesetih godina se sa paradigme zasnovane na zaključivanju preSlo na novu paradigmu zaisnovanu na znanju. Oblast delovanja istraživača inienjerstva znanja postaje Istovetna sa oblastima delovanja stručnjaka iz pojedinih uskih oblasti: prikupljanje specifičnih znanja i iskustava, te poton i njihova primena u reSavanju odredene grupe problema. Preduslov za ovakvo, heurističko, reSavanje problema Je Izbor pogodne reprezentacije relevantnog znanja kome inteligentni program može l£>ko da pristupi, dok mehanizam zakl juCi vatnja, t J. mehanizam koriščenja taiko memorisanog znanja treba da Je jednostavan i zasnovan na tom znanju umesto na opStlm principima ili nekakvim funkcijama komplIkovanim za izračunavanje. Ljudsko znanje se kodira određenim metodama u module koji se u mehanizmu zaključivanja aktiviraju uzorcima: "sirovi" podaci, "obrađeni" podaci, patrcijalna reSenJa, neočekivane situacije, greSke i si. Ovakvi uzoračko vođeni moduli imaju niz prednosti u odnosu na nekakav opSti algoritam zaključivanja: -predstavljanje znanja u delovlma Je primerenlji načinu memorisanja znanja eksperata, -programiranje sa ovakvim modulima omogudava razvoje inteligentnih sistema u koracima, programi se iako modlfikuju i proširuju, a greSke unutair znanja se popravljaju bez izmene koda programa, i si. Proces konstruisanja Jednog inteligentnog sistema obuhvata sledečih pet oblasti: -prikupi Jau-iJe 1 sistematizacija relevantnog znanja: od eksperta ili naSinsklm učenjem na primeriiiia, -reprezentacija znanja: izbor pogodnog načina kojim se velika količina znanja može predstaviti pomoču simboličkih struktura podataka unutar raCunara, pogodnih za zakl JuCl vóinje. Odabrana struktura treba da omoguCi fleksibilne izmene i dopune memorlsanog znanj a, -primena znauija: planiranje 1 kontrola reSavanJa problema, heurističko zaključivanje, taCnost i efikasnost rada Inteligentnih procesa, koje memorisano znanje predstavlja, -generiszinje obJaSnJenJa: interakcija računal—čovek, objašnjenje zaSto Je problen reSen na Jedan a ne na neki drugi naCin, mogućnost učenja na greSkama i utlcanja čoveka na proces zaücl j uč i vanj a, -obrazovanje: smeSteno znanje se uz izvesne ograde može koristiti 1 za stvatr^Je inteligentnih sistema uCenja. 3. INZENJERSTVO ZNANJA 1 OBRAZOVANJE RaCunsir u obrazovanju sa stanovišta nastave se može posjnatrati kao novo nastavno sredstvo i kao upravljač nastavnog procesa. Za razliku od konvencionalnih nastavnih sredstava Cgrafoskop, diaskop, interna televizija, responderi i dr.J raCunar u nastavni proces unosi znaCaJnu novinu mogućnost obostrane komunikacije raCunar -uCenik. Nijedno od konvencionalnih nastavnih sredstava ne može da odgovara na pitanja uCenika i da na taj naCin usmerava nastavni proces. JCao upravljač nastavnog procesa, radunar u obrazovanju se posmatra kao neposredni izvrSioc nastavnog procesa kreiranog putem programske podrSke i upravljač raznih pomoćnih uređaja nastavnog procesa elaboratoriJski uređaji, responderi i dr.). Ovako posmatrana primena raCunara u obrazovnom procesu otvara moguilnost pri mena metoda i tehnika inienjerstva znanja u obrazovanju i otvara novo polje istraživanja - projektovainje inteligentnih sistema uCenJa. Projektovanjo ovakvih sistema uCenJa zahteva interakciju metoda inienjerstva znanja sa Jedne strane i metoda pedagogije, metodike, didaktike i psihologije sa druge. notacijskog sistema ostaje da izabere najpogodniju strukturu podataka koja se implementira zadržavajući sve dobre osobine izabranog notacijskog sistema. Važni krlterljuml za izbor notacijskog sistema i organizaciju podataka za reprezentaciJu znanja su; -logička dovoljnost tJ. da rornalizan može na pogodan naCin da opl£e znanje, -efikasnost pristupa pri obradi znanja, -iskoristivost, tJ. reprezentovano znanje se može upotrebi ti u resavaiiju problema za koje su ta znanja dovoljna. Za reprezentaciju znanja u priraenl inženjerstva znanja se koriste sledeći formalizmi: produkcijska pravila, strukturni objekti i predikatska logika. Svi navedeni formalizmi se implementiraju sami ili u nekoj kombinaciji, u uzoraCko vođenim sistemima. Struktura podataka koja pretstavlja unutrašnju reprezentaciju izabranih formalizaxia pretstav1 janja znanja je zavisna od problema koji se reSava, sistema zaklJuCivanja, interpretatora mehanizma procesiranja znanja, raCunara na kome se implementira i programskog Jezika izabranog _za realizaciju određenog inteligentnog sistema. Pretpostavka da se znanje koje sadrže ekspertni sistemi standardnog tipa može iskoristiti i u svrhe obučavanja, deraantuje se u praksi Jer su takvi inteligentni programi loSi uCitelJi 141. Uzrok je upravo izostavljanje osnovnih principa pedagogije i metodike pri kreiranju programskih sistema CiJa je svrha prvenstveno konsultanska pomoC pri reSavanju problema. Kreiranje posebnih inteligentnih sistema namenjenih obrazovanju, mora reälti sledeCe probi eme: -kako predstaviti znanje koje uCenik treba da usvoji, -kako opisati pojmove koji se usvajaju, -kako usaglasiti mehanizam koriSCenJa takvog znanja sa metodičkim i pedagoškim principima usvajanja znanja, -kako iskoristiti dobre osobine svih vrsta konvencionalnih naCina prenošenja .1 usvajanja znanja: predavanje, testiranje, eksperiment, opažanje, programirana nastava i dr. 4. SISTEMI REPREZENTOVANJA ZNANJA Znanje se može definlsati kao simbolička reprezentacija Činjenica i relacija među njima. Reprezentacija znanja je naCin predstavljanja znanja, kao i naCin kako se ono može povezivati sa drugim znanjem, koristiti za reSavanje novih situacija i izvoditi novo znanje. U ISJ reprezentacija znanja se definiSe kao skup sintaksnih i semantičkih konvencija koje omogućavaju opisivanje stvari. Sintaksa reprezentacije Je skup pravila za formiranje, kombinovanje i uređenje izraza u jeziku reprezentacije. Semantika reprezentacije određuje kako se sintaksno valjani izraz koji reprezentuje znanje interpretira, tj. kako se iz date forme može izvesti i koristiti znanle. Reprezentacija znanja Je bitan element inženjerstva znanja koji omogućava sistematičan naCin kodiranja znanja struCnjaka o nekom problemu unutar neke Sire kategorije. Ona implicitno obuhvata i organizaciju podataka u raCunaru za memorisanje znanja. Postoji niz notacijskih sistema za predstavljanje znanja u raCunaru. Zajednička Icarakteristlka svih je da treba da obezbede brz pristup znanju i da se znanje može lako koristiti pomoću manje-viSe prirodnih mehanizama zaključivanja ili izvođenja. Programeru nakon odaiblranja Sistemi koji koriste neki od navedenih formalizama, se sastoje od niza relativno nezavisnih modula koji omogućavaju prikupljanje i memorisanje znanja, formiranje odgovarajuće unutrašnje reprezentacije znanja, koriSćenje prikupljenog znanja 1 si. Produkcijska pravila su formalizam za predstavljanje znanja koji se koristi i u teoriji automata, formalnim jezicima i dizajniranju programskih jezika. Saistoje se od skupa pravila oblika: if cp, a . . . A p > then a . . . A a Ini m gde su Pj , 1=1, . . . ,n uslovl, a Aj , j«l, . . . ,m zaključci.Uslovi su trojke objekt - atribut -vrednost oblika: CBor Je_rudnlk bakar> dok su zaključci akcije koje se preduzinaju ako su uslovi zadovoljeni. KoriSćenjem ovog formalizma kodiraju se iskustvene veze . i m Predikatska logika, u CiJoJ osnovi je propozicioni i predlkatski raCun, razvojem logičkog programiranja i logičkih programskih Jezika, se koristi 1 kao sistem predstavljanja znanja. Znanje se predstavlja pomoću formula, kao napr.: Svako voli nekog <==> i markerlma teorije okvira C"frane">, ill otvorima 1 puniocima C'fllier'O konvencionalnih struktura podataka tipa slog. Oni obuhvataju sledeCe formalizme: semantičke Casoc1Jativne mre2e>, okvire, objektno orjentlsane sisteme, strukture konceptualne zavisnosti 111 skripte. Predlkatska logika i produkcijski sistemi kao formalizmi predstavljanja znanja se koriste za reprezentovanje različitih aspekata okoline. Međutim, u opStem sluCaJu, oni ne dozvoljavaju da struktuirarao znanje o toj okolini. Strukturni objekti ukiJuCuJu noguCnost reprezentovanja strukture znanja, grupisanjem delova znanja u celine i relacija među znanjem, kao i pokazivača na akciju koja se preduzima koriščenjem tog znanja. Takode se »anutao-strukturnih objekata predviđa rad sa podrazumevanim Cdefault3 vrednostima, otkrivanje greäaüca kao i rad sa nepotpunim znanjem. Sve ove nabrojane osobine su direktno primenljlve u predstavljanju znanja za obrazovne svrhe. 5. PREDSTAVLJANJE ZNANJA U SISTEMU OSOF Znanje za potrebe obrazovanja se može organlzovati u nastavne sekvence . filanak sadrži minimalnu količinu zaokruženog znanja koga učenik treba da savlada u Jedinici vremena. Svaki Članak se sastoji od naziva, teksta kojim je on opisan, grafičke ilustracije ili simulacije i proizvoljnog broja zadataka kojim se može proveriti 1 utvrditi znanje opisano u danku. Zadatak Je opisan tekstom, slikom ill simulaciJörn, a odgovor se mo2e eksplicitno uneti, odabrati od niza ponuđenih alternativa 111 odabrati iz dve grupe ponuđenih alternativa, uparivanjem. Alternative su opisane tekstom, a svaki moguci odgovor sadrži 1 informaciju o daljem toku uCenJa u sluCaJu da Je uCenik odgovorio na odgovarajući naCin ili odabrao određenu alternativu kao svoj odgovor na postavljeni zadatak. U sistemu OSOF iskoriSCena Je metoda okvira za pretstavlJanje ovako organizovanog znanja. Okvir se sastoji od skupa imenovanih slotova koji sadrže vrednosti ili pokazivače na druge okvire [53. Struktura podataka koja odgovara navedenoj reprezentaciji i organizaciji znanja zapisana u pseudo Jeziku za opis okvira Je: Begin Sekvenca < Ime: Niska; F PoCetaik: Članak > Begin Članak { Pojam: Niska; Opis: Niska, Simulacija, Slika; F Pitanje: Zadatak > End; Begin Zadatak < Opis: Niska, Simulacija, Slika; F SledeCi: Zadatak; F Odgovor: Alternativa > End; Begin Alternativa < Opis: < Izbor, Otvoreni odgovor, Uparivauije ); F Akcija: < Članak, Zadatak. Dopuna_op i sa, Kraj > ; F Sledeći: Alternativa > End; Begin Kraj < Ime: Niska; F Akcija: < Sekvenca, Članak, 'Exif > > End; U okvirima Sekvenca, Članak, Zadatak i Kraj "Niska" označava tekst proizvoljne dužine, "Simulacija" proceduru za •simuliranje nekog procesa, a "Slika" proceduru za grafički prikaz proizvoljne slike. Unutar okvira Alternativa noguđi zadaci koje uCenik treba da izvräi su: "Izbor" - na postavljeni zadatak se odgovara izbor jedne od navedenih alternativa, "Otvoreni odgovor" - zahtev za ekspllctni upis refienja 1 "Uparlvanje odgovora" - postavljeni zadatak se reSava uparivanjem odgovarajućih alternnativa iz dva skupa. Na osnovu uCenikovog reSenja zadatka, akcija rafiunara se odvija prelaskom na: Jedan od okvira Članak, Zadatak 1 Kraj, 111 grupu okvira Članak koji pružaju dodatno objašnjenje nejasnog opisa C"Dopuna opisa">. Oznaka F ispred imena slota oznaCava da je njegova vrednost pokazivač na okvir. 6. SISTEM OSOF Sistem OSOF 131 Je razvijen u .Institutu za matematiku u Novom Sadu i saistoji se iz modula za prikupljanje znanja TEA, njegovu internu reprezentaciju po opisanoj Semi 1 dva modula elementarnog koriSCenJa za usvajanje znanja: izborom alternativa - LEA i testiranjem - EXA. Realizovan je programom vodenim menijima i izuzetno Je Jednostavan za korlSCenje, te od nastavnika i uCenlka ne zahteva nikakvo znanje o ustrojstvu raCunara - niti znanje prograuniranja. Primenom sistema zaključeno je da je odaibrana. metoda okvira pogodna za prlmenu u obrausovanJ u. LITERATURA: 1. Barr A., Feigenbaum E. A., Handbook of Artificial Intelligence, Stanford University Computer Science Dept, Stanford, <19805, USA 2. Buchanain B. Q., Feigenbaum E. A., Dendral and Meta-Dendral: their applications dimension. Artificial Intelligence, lia,2>, 5-24, <19785, USA. 3. PauniC D., Jerinlć Lj. , Budlraac Z., IvanoviC M., Univerzalni programski paket za primenu raCunara u nastavi, u Stampi. 4. Clancey V. J., Methodology for building an intelligent tutoring system, from "Methods and tactics in Cognitive Science", Lawrence Erlbaum Publishers, <19835, USA. 5. Frost R. , Introduction to Knowledge Based Systems, Collins, London, <19865, Great Britain. 6. IvanoviC M., Jerinlć LJ., Paunid D. , Bud1mac . Z., On knowledge representation in education. Review of research. Institute of Mathematics, Novi Sad, <19885, je postala tudi bolj globalna kot kdaj koli poprej: na to so vplivale sile trga, pretok kapitala in tehnološki imperativ. Padec prodaje v ZDA in cenejši dolar sta pospešila mednarodno poslovno aktivnost ameriških informacijskih podjetij. Tako je podjetje IBM že drugo leto prodalo več v tujini kot doma. Še več, dejanska rast prodaje IBMa je bila dosežena zunaj ZDA. Skupaj je že 14 ameriških podjetij od stotih doseglo več kot polovico dohodka na zunanjem trgu, med njimi tudi DEC, HP, NCR, Tandem Computers in Microsoft. Podjetje Compaq pa je povečalo prodajo v Evropi za 145% in se je v Evropi uvrstilo med 25 največjih informacijskih proizvajalcev. Vendar je zanašanje na šibek dolar postalo dvomljiva opora v dolgoročnem planiranju, saj se je že spomladi 1. 1989 dolar okrepil in tako so se zmanjšale tudi močnosti za prekomorsko prodajo ameriških proizvajalcev. Evropska razvojna scena V Evropi so znanilci unifikacije evropskega trga po letu 1992 spodbudili preobrat v meddržavnih zve?ah. Evropska podjetja, ki so bila doslej prilagojena zaščiti domačih trgov, morajo hitro privzemati merila in upravljavsko iznajdljivost, da bi bila ustrezno pripravljena za novo obliko odprtosti evropskega trga. Finsko računalniško podjetje Nokia je danes eno najaktivnejših evropskih podjetij (sll65m dohodka v 1. 1988), ki je pridobilo posle sosednjega, švedskega podjetja LMEricson Telephone Co. in se razgleduje v Zapadni Nemčiji z namero, da prevzame mesto televizijskega proizvajalca. Siemens AG je sklenil strateški telekomunikacijski dogovor z italijanskim Italtel, od IBMa pa je v ZDA odkupil podjetje Rolm. Siemens si je dovolil tudi množično reorganizacijo podjetja v 1. 1988, podobno kot Olivetti in s podobnim ciljem: s sploščitvijo korporativne piramide in z večjo prožnostjo tržnega reagiranja. Britanski STC PLC, v katerem ima Northern Telecom 24%-ni delež, je prevzel od NT termi- nalski posel in onstran Atlantika še miniraču-naknigkega proizvajalca Computer Consoles in operacije podjetja Datachecker v sestavi National Semiconductor Corp. Druga največja evropska softwarska in storitvena hiša je nastala z združitvijo britanskih podjetij Systems Designer in Scicon International za francoskim podjetjem Cap Gemini Sogeti. Podobno sta se okrepili in razširili svojo mednarodno dejavnost tudi italijansko softwarsko in storitveno podjetje Finsiel SpA in francosko izposojevalno podjetje Europe Computer Systems, ki je. last francoske Bank Societe Generale. Nevarnost prevelikega vztrajanja računalniškega proizvajalca na domačem trgu je dobila svoj epilog v podjetju Norsk Data AS, pri katerem se je pokazala izguba že v 1. 1988, ko je to podjetje v domačem okolju izgubilo ključne strateške posle v konkurenci s podjetji Apple, DEC, IBM in Buli. Po mnenju izvedencev sta tako Norsk Data kot nemški Comparex Informationsysteme GmbH podjetji, ki se morata čimprej iz-zviti iz prekomerne odvisnosti njunih domačih baz. Podobna ugotovitev velja tudi za jugoslovanskega računalniškega proizvajalca Iskro Delto, ki se je v preteklem in letošnjem letu sicer preusmerjala v mednarodne posle, vendar se je kljub temu znašla v podobnih težavah. Japonci motrijo globalna tržišča Tudi japonska podjetja se vmeščajo v novo-nastajajoča globalna tržišča. Do sredine osemdesetih let je bila japonska proizvodnja usmerjana na izvozne trge, ta trend pa je bil obnovljen zopet v letu 1988. Nujnost take usmeritve je bila pogojena z močjo jena in z bojaznijo trgovinskih omejitev tako na evropskem kot ameriškem trgu. Japonsko podjetje Alps Electric je napovedalo gradnjo tovarne v Zapadni Nemčiji in razširitev svojih operacij v ZDA. Podjetji Seiko Epson in Fujitsu sta napovedali nove tovarne v Britaniji, podjetje Mitsubishi Electric pa svoje zastopstvo in tovarno v Franciji. Med prvimi 100 računalniškimi podjetji na svetu najdemo kar 17 japonskih in daljnjevzhod-nih podjetij, 22 jih je iz Evrope in 61 iz ZDA. Med prvimi desetimi na svetu so tri japonska (Fujitsu, NEC, Hitachi),le dve evropski podjetji (Siemens in Olivetti) in pet ameriških (IBM, Digital, Unisys, HP, NCR). Teh deset podjetij -ob čakanju podjetja Croupe Bull, da se mednje povzpne - oblikuje novo informacijko oziroma računalniško hunto. Teh deset podjetij obvladuje več kot polovico celotnega informacijskega trga (v 1. 1988), pri čemer odpade samo na IBM 22,6%. Rast teh globalnih informacijskih velikanov pa že vzbuja skrb možnosti destruktivnega trgovinskega spopada. Ta spopad se je v preteklosti pokazal kot možnost med ZDA in Japonsko, po letu 1992 pa se na spopadnem prizorišču pojavlja še Evropa. Naraščanje globalne kooperacije Izkugnje iz trgovinskih spopadov kot globalne konkurence med podjetji pa odpirajo tudi možnost čedalje pomembnejše usmeritve: naraščanje stopnje globalne kooperacije med danes največjimi multinacionalnimi podjetji. Skladno s tem scenarijem pa ni največji strah teh podjetij v medsebojni konkurenci temveč v nastajanju malih podjetij na njihovih domačih trgih, saj prav ta podjetja razvijajo inovativne produkte in osvajajo nenavadne deleže na trgu. Prav v okviru teh pojavov je mogoče iskati nove načine globalne konkurence med evropskimi, japonskimi in ameriškimi multinacionalkami (glej npr. K. Ohmae, Triad Power, Free Press, 1985). Danes je povsem jasno, da želijo vodstva globalnih podjetij zaščititi svoj poločaj na domačem trgu z vsemi sredstvi in tudi tako, da pristajajo na konkurenco iz območja globalne triade kot prednostjo, ki jo ima sporazumevanje pred destruktivnim trgovinskim spopadom. V zadnjem letu je rast informacijskega trga v ZDA znašala le 8,4%, medtem ko je dosegla v Evropi 14,5% in v azijsko-pacifiškem prostoru, vključno z Japonsko, 29%. Ameriška rast je upadla predvsem zaradi čedalje večje nepopularnosti velikih sistemov. Tako so prav IBM, CDC, NCR in Unisys poudarjali prav prodajo main-framov, ki je na ameriške trgu upadla. Japonci so še vedno dosegli 20% povečanje prodaje main-framov na domačem trgu, v ZDA pa je le podjetje Amdahl povečalo prodajo svojih procesorjev za 32,3%. Pričakovati je, da bo prodaja velikih sistemov §e naprej upadala. Bolehni minij i Prodaja miniračunalnikov, vključno z delovnimi postajami, je bila proti pričakovanju nezdrava. V ZDA se je Digital dokončno slabo odrezal (oplel), dočim sta bili podjetji Wang Labs in Data General pozitivno slabokrvni. Veliki evropski (finski) miniračunalniški proizvajalec Nokia (ki je prevzel informacijske posle podjetja Ericson) in norveški Norsk Data sta imela slabo letino. V svetovnem merilu je prodaja miniračunalnikov narasla le za 8% pri rasti celotnega informacijskega trga za 10%. Vse pozornosti vredno pa je ostalo področje procesiranja sprotnih transakcij (PST), ki predstavlja že enega od dveh prodanih sistemov. Stagnirajoče zmogljivosti mainframovskih in miniračunalniških segmentov naj bi dokazovale, da je področje informacijskih sistemov stopilo v svojo zrelo fazo. Vendar pomeni v nekaterih industrijskih segmentih, kot je npr. software, dozorevanje tudi rast, ki se bo nadaljevala. Prodaja softwara je narasla za 22,3% in je dosegla s20,8bn. Rast podjetja Oracle s 114,4% je na področju softwara edinstvena. Podjetje Oracle zelo uspešno upošteva standarde, odprto arhitekturo in pomanjševanje, s katerimi so obsedena velika podjetja. In Oracle odkriva tržne niše, ko uporabnikom pojasnjuje svojo filozofijo. Dohodek računalniških storitvenih podjetij se je povečal za zdravih 23,1% (upoštevajoč 100 najboljših), ko so ta podjetja vstopila v področje t.i. sistemske integracije. To velja tako za Evropo kot za ZDA. Tu se skrivajo tudi največje trenutne možnosti rasti domače računalniške industrije. Moč mikroračunalnikov Največja pozornost se posveča še vedno področju mikroračunalnikov. Kljub občutnemu pomanjkanju pomnilniških integriranih vezij je podraja narasla za pomembnih 26,8% in dosegla če 11,7% celotne računalniške prodaje, tako da se že približuje prodaji mainframov. Podjetja Compaq, Apple, Toshiba in Zenith Electronics so v preteklem letu znantno napredovala. Podjetje Apple je v ZDA že prehitelo IBM v tržnem deležu prodaje PCjev glede na mlačen sprejem IBMovega PS/2 in njegovo prehitro umaknitev ATja. Napre- doval je tudi Atari, ki proda 85% proizvodnje v Evropi in podjetje AST Research (s katerim sodeluje tudi naša domača industrija). Močno pa se pojavljajo tudi tajvanska in korejska podjetja. Tako je tajvanski Acer prodal že za $300m PCjev. Trg računalniške periferije je dosegel v preteklem letu vrednost $61,8bn s prehodom na 3,5 eolske diskovne naprave. Prodaja naprav za podatkovno komunikacijo, ki vključuje kominika-cijske procesorje, javne centrale, modeme, mul-tiplekserje itd. je narasla le za borih 6,7% na vrednost $16bn v letu 1988. Podjetje AT&T je investiralo $6,7bn v digitalizacijo svoje mreže; ta proces naj bi se končal do 1. 1992, Podjetje Northern Telecom je investiralo $200m v rekonstrukcijo izdatkov in napovedalo svoj prodor v Evropo in Azijo zaradi splosčitve trga v Severni Ameriki. Računalniško vzdrževanje ostaja pomemben vir dohodkov informacijskih podjetij, saj je v 1. 1988 doseglo dohodek s30bn. V to kategorijo sodi tudi izposojanje računalnikov, ki pa ni več tako donosno, kot je bilo poprej. V tej povezavi so zanimivi tudi podatki o izgubarjih. Med 100 največjimi računalniškimi podjetji je tudi 10 izgubarjev, in sicer: dva proizvajalca miniračunalnikov (Data General in Norsk Data) zaradi prevelike navezanosti na domače tržišče; dva proizvajalca diskov (Micropolis in Seagate Technology), ki sta napačno ocenila hitri pomik v to tržišče itd. K;:.cunalniško podprto obliko-venje in proizvodnja (CAD/CAM) sta prav tako napredujoči področji in z njima deiovne postaje, kjer je podjetje Hewlett-Packard naredilo bistven prodor, z njim pa v Evropi tudi finski Nokia (z nakupom Ericsonovih operacij). Neuresničene integracije Med zanimivimi povezavami, ki naj bi se uresničile, vendar se niso,' so npr. tele; za NCR je bilo rečeno, da je v interesnem polju najprej podjetja Unisys, potem pa AT&T. Za Apple in Cray Research se je predpostavljalo, da sta idealna partnerja, podobno se je ugotavljalo tudi za Wang in Xerox. Xerox naj bi s tem prestrukturiral svoj marketing posebno na področju izdajateljskih sistemov. Medtem ko se združevalna obsedenost v računalništvu ni uresničila pa se je oblikoval kritičen pogled na razrahljano zaupanje dejavnosti raziskav in razvoja (R&D)-. Velja poudariti, da se je za raziskave in razvoj ponekod še vedno izločalo do 15% dohodka, vendar je povprečje v primerjavi s prejšnjim letom zdrknilo iz 10,9% na 9,9%. To upadanje R&D v ZDA se dogaja v žasu, ko Japonci ponovno oživljajo dejavnosti R&D na globalni ravni! NEC je odprl svoj Research Institute v Princetonu, NJ, podjetja Epson, Hitachi in Canon pa R&D enote v Evropi in ZDA. Od ameriških podjetij le IBM ni spreminjal svoje R&D strategije s svojo R&D prisotnostjo širom po svetu. Študija ustanove National Science Foundation kaže, da namenjajo ameriška podjetja več sredstev za R&D dejavnosti v tujini. Po vsem tem je mogoče ugotoviti, da je bila ameriška strategija na začetku osemdesetih let globalna; ozadje tega je bil najhitreje rastoči ameriški trg. Danes temu ni več tako. Pobudo prevzemajo Japonci in Evropa, medtem ko je ameriško tržišče uravnoteženo. A. P. Železnikar Poslovni podatki za računalniška podjetja na svetu v koledarskem letu 1988 v spodnji preglednici so zbrani prihodki nekaterih računalniških podjetij po svetu za leto 1988. Ta preglednica daje razvrstitev največjih računalniških podjetij in v njo so uvrščena tista podjetja, ki bi za domačo strokovno (beri poslovno) javnost lahko bila zanimiva. Nekaj vodilnih računalniških podjetij glede na prihodek v preteklem letu Mesto Podjetje Prihodek 1 IBM US$ 55 002,8m 2 Digital Equipment 12 284,7m 3 Fujitsu 10 999,1m 4 NEC 10 475,7m 5 Unisys 9 100,0m 6 Hitachi 8 247,6m 7 Hewlett-Packard 6 300,0m 8 Siemens (Muenchen) 5 951,0m 5 Olivetti (Ivrea) 5 427,5m 10 NCR 5 324,Om 11 Croupe Bull (Paris) 5 296,7m 12 Apple 4 434,1m 13 Toshiba 4 226,6m 14 Matsushita 3 441;0m 15 Canon 3 391,6m 16 Control Data 3 254,5m 17 Wang 3 074,4m 18 Nixdorf (Paderborn) 3 044,9m 19 NV Philips (Eindhoven) 2 794,6m 20 Xerox 2 650,Om 21 AT&T 2 445,Om 22 STC (London) 2 425,1m 23 Memorex Telex (Amsterdam) 2 078,5m 24 Compaq 2 065,6m 28 Amdahl 1 801,8m 31 . Alcatel (Paris) 1 716,0m 37 Sun Microsystems 1 461,6m 41 Atlantic Computer- (London) 1 341,6m 46 Inspectorate International (Neuchatel) 1 230,3m 47 Societe Generale (Paris) 1 222,6m 50 Nokia (Helsinki) 1 165,Im 53 Cap Gemini Sogeti (Paris) 976,5m 57 Econocom (Amsterdam) 897,0m 59 Amstrad (Essex) 841, Cm 62 Alps 785,2m 63 Mannesmann Kienzle (Duesseldorf) 779,0m 66 Microsoft 718,9m 73 Comparex IS (Mannheim) 614,5m 77 Racal Electronics (Berkshire) 554,1m 78 Finsiel (Roma) 545,4m 82 Lotus 468,5m 83 AST Research 459,0m 85 Norsk Data (Oslo) 450,2m 90 Oracle 424,6m 92 Acer Group (Tajpeh) 379,4m 94 Sema Group (London) 375,1m 95 SD-Scicon (Hampshire) 366,4m Skupno v 1. 1988 (100 vodilnih podjetij) USs 243 100,Om Zanimivo je, koliko od navedenega skupnega prihodka so realizirala posamezna geografska področja oziroma države. Oglejmo si tole tabelo: Podjetje/država Prihodek od celote $243,Ibn IBM 55 002,Bm 22,626% Japonska 53 528,Om 22,019% Evropa 40 094,3 16,493% ZR Nemčija 10 389,4m 4,274% Francija 9 211,8m 3,789% Italija 5 973,3m 2,457% Združeno kraljestvo 5 904,Im 2,429% Nizozemska 5 770,Im 2,374% Skandinavija 1 615,3m 0,664% Švica 1 230,3ra 0,411% Pri tem je treba seveda upoštevati, da v tej preglednici ni podatkov s področja Vzhodne Evrope, kjer se nahajajo nekatera velika računalniška podjetja, ki bi lahko v naslednjem obdobju bistveno preobrnila prihodkovno težišče v korist Evrope, in sicer tako finančno kot tržno / razvojno. Danes sta v Evropi podjetji Siemens in Olivetti domala prihodkovno izravnani in na računalniškem področju bi se lahko ponovila zgodba iz avtomobilske industrije (Volkswagen in Fiat). Seveda pa ne gre podcenjevati tudi drugih evropskih proizvajalcev, zlasti podjetja, kot so francoski Croupe Bull, nemSki Nixdorf, nizozemski NV Philips, britanski STC, nizozemski Memorex Telex itd. A. P. Železnikar Izgubarji in nazadovalci v računalniški industrgi v letu 1988 v letu 1988 so nekatera znana računalniška podjetja pridelala tudi izgubo: Mesto Mesto med 100 Podjetje Izguba v 1988 21 98 42 85 99 52 .AT&T US$ 1 669, Om Atari 84,8m Data General 48,9m Norsk Data 41,6m Micropolis 19,4m National Semič. 18,Im Seveda so zanimivi tudi podatki o podjetjih, ki so nazadovala: M MIOO Podjetje 198B 1987 % 1 31 Alcatel ECUl 450,Om 1 780,Om 18,5 2 109 Tandon $ 309,3m 374,Om 17,3 3 68 General Elee. 675,Om 750,Om 10,0 4 118 Gould 275,Om 299,3m 8,1 5 77 Racal Elee. P 311,4m 335,8 7,3 8 46 Inspectorate Internetional FFl 800,Om 1 835,3 1,9 Največji prihodek na zaposlenega v računalniški industrii leta 1988 V letu 1988 so nekater računalniška podjetja, zbrana v razpredeli\ici, dosegla tele prihodke na zaposlenega: Mesto Podjetje Prihodek Število med na celoten zapos. 100 zapos. 1 41 Atlantic Computers $937,5k $1341 , 6m 1431 2 57 Econocom International $560,6k $ 897 , Om 1600 3 73 Comparex $545,3k $ 614 , 5m 1127 4 12 Apple $409,2k $4434, , lm 10836 5 24 Compaq $344,3k $2065 , 6m 6000 6 54 Commodore $ 2 7 4,Ok $ 926 ,1m 3380 7 25 Nihon Unisys $270,2k $2057 , 7m 7616 8 83 AST Research s226,7k S 459 ,0m 2025 9 28 Amdahl .$217,Ik $1801 ,8m 8300 10 66 Microsoft $205,3k $ 718 , 6m 3500 11 82 Lotus $182,8k $ 468 , 5m 2563 12 37 Sun Microsystems $177,Ik $1461 , 6m 8253 13 38 Tandem Computers $162,9k $1424 ,7m 8745 14 81 Wyse Technology $152,7k $ 488 ,7m 3200 15 71 Apollo Computer $147,Ok ä 653 , 5m 4446 Zanimivo je, da dosegajo največji prihodek per capita prav nekatera evropska podjetja, tj. prvi Atlantic Computers (ZK), drugi Econocom International (Nizozemska) in tretji Compare* (ZR Nemčija). Povprečni prihodek per capita najboljših petnajstih znaša s320,8k pri 73022 zaposlenih. Tabelarično imamo: Podjetje /skupina Atlantic Computers prvi trije prvih pet prvih deset prvih petnajst Prihodek per capita $937,5k S681.1k S559,2k $399,Ok $320,8k Število zaposlenih 1431 4158 20994 45815 73022 Pri tem je morda zanimivo, kakšen prihodek per capita iz računalniških dejavnosti so dosegli največji: M Podjetje Prihodek Število per capita zaposlenih 1 IBM $154,2k 387112 2 Digital Equipment S 98,8k 124400 3 Fujitsu $116,Ok 94825 4 NEC $ 99,3k 105486 5 Unisys $106,5k 93000 6 Hitachi $ 56,2k 161000 7 Hewlett-Packard $113,Ok 87000 8 Siemens $ 16,9k 353000 9 Olivetti $ 94,3 57560 10 NCR 11 Croupe Bull 12 Apple" $ 99,8k $116,3 $409,2 60000 45557 10836 Računalniška podjetja z največjo rastjo prihodka v letu 1988 Seveda velja omeniti, da je to le prihodek per capita iz računalništva in da niso upoštevani dohodki iz drugih dejavnosti podjetij v razpredelnici (npr. pri IBMu-, Fujitsu, Hitachi-ju, Siemensu itd.) A. P. Železnikar Računalniška podjetja z največjo donosnostjo v letu 1988 Donosnost je mogoče ocenjevati z več vidikov. Oglejmo si dve vrsti donosnosti (return), in sicer donosnost iz prometa (prodaje) (return ■on sales) in donosnost celotnega kapitala oziroma poslovnih sredstev (return on assets). Donosnost iz prometa: M MIOO Podjetje 1988 1987 1 66 Microsoft 21,1% 20,4% 2 64 Cray Research 20,7% 21,4% 3 55 Computer Associates 15,4% 9,3% 4 59 Amstrad 14,9% 17,9% 5 90 Oracle 14,6% 15,0% 6 82 Lotus 12,6% 18,2% 7 28 Amdahl 12,4% 9,7% 8 24 Compaq 12,4% 11,1% 9 33 Automatic Data Processing 11,0% 10,2% 10 60 Intergraph 11, 0% 10,9% 11 2 Digital Equipment 9,8% 12,4% 12 1 IBM 9,7% 9,5% 13 12 Apple 9,5% 9,2% 14 7 Hewlett-Packard 8,3% 8,0% • 15 97 Diebold 7,9% 8,1% Donosnost celotnega kapitala oziroma donosnost poslovnih sredstev: M MIOO Podjetje 1988 1987 1 41 Atlantic Computers 31,3% 52,7% 2 59 Amstrad 30,4% 46,6% 3 66 Microsoft 25,0% 32,3% 4 91 Science Applications 24,0% 8,4% 5 90 Oracle ■ 18,5% 16,0% 6 12 Apple 18,4% 17,3% 7 24 Compaq 16,1% 15,1% 8 64 Cray Research 15,8% 16,3% 9 82 Lotus 14, 0% 22,7% 10 55 Computer Associates ■12,3% 7,7% 11 2 Digital Equipment 11,8% 13,6% 12 78 Finsiel 11,7% 15,6% 13 28 Amdahl 11,6% 9,7% Bilo bi koristno, če bi se pri zadnjih dveh razpredelnicah zamislili tudi naši ekonomisti in finančniki, ko bi na podoben način ocenjevali donosnost domačih podjetij, še zlasti po številnih reorganizacijah v naši elektronski industriji. A. P. Železnikar Čeprav se pri nas lahko čudimo vsakršnji ekonomski rasti domačih podjetij pa nekatera računalniška podjetja v razvitem svetu izkazujejo prav to, čemur bi pri nas rekli prihodkovna megalomanija. Seveda ni mogoče kar tako odgovoriti, kako jim to uspeva. Petnajst prihodkovno najbolj rastočih računalniških podjetij je zbranih v naslednji preglednici: M MIOO Podjetje prih.■ prih. % 1988 1987 1 50 Nokia Fmk4877m 1835m 165, 8 2 88 Nynex S 430m 180m 138, 9 3 90 Oracle. s 425m 198m 114, .4 4 37 Sun Microsystems $1462m 756m 93, 4 5 94 Sema : FS 211m 121m 74, .8 6 67 Continental Info .S 698m 405m 72, ,3 7 24 Compaq $2066m 1224m 68, ,7 8 74 Miniscribe $ 603m 363m 66, ,4 9 34 Prime Computer $1594m 961m 65, ,9 10 49 Arthur Andersen $1199m 749m 60, ,0 11 83 AST Reasearch ■ $ 459m 290m 58, ,4 12 66 Microsoft $ 719m 457m 57, ,4 13 12 Apple S4434m 3041m 45, ,8 14 98 Atari $ 362m 250m 44, ,7 15 55 Computer Assoc. $ 925m 649m 42, ,6 Finski Nokia in britanski Sema sta evropska rekorderja v prihodkovni rasti, razvidno pa je tudi, kako se dobro drčijo znani mikroraču-nalniSki proizvajalci (Compaq, Apple in Microsoft). Kdaj bomo lahko začeli'zbirati podatke o prihodkovni rasti naših računalniških podjetij tudi pri nas (seveda na dolarski ali markini osnovi)? A. P. Železnikar IBM v preteklem letu Za predsednika podjetja IBM Johna Akersa (IBM CEO) pravijo, da je postal partner partnerjev. IBM (Old Orchard Road, Armonk, NY 10504) je v preteklem letu dosegel računalniški prihodek 55 002 800 000 dolarjev, in sicer 42% v Severni Ameriki, 36% v Evropi, 15% v Aziji in na Pacifiku in 7% drugje. Značilnost njegove politike je bila partnerstvo s tekmeci. Če je bilo leto 1987 leto uporabnikov, je bilo leto 1988 leto partnerjev. Proti strategiji AT&T je IBM reagiral skupaj z Digitalom z medpodjetniškim konzorcijem za Unix. Svoja zaščitena integrirana vezja je ponudil tako miniproizvajalcu Digitalu kot prizvajalcu mainframov Siemensu, ki je v Evropi glavni tekmec IBMa.. S Siemensom je sklenil skupne marketinške posle, pri čemer je Siemensu prodal telekomunikacijsko podjetje Rolm. Drugi bistven dogovor je bil sklenjen z bivšim predsednikom podjetja Apple glede pravic uporabe uporabniško prijaznega vmesnika podjetja NeXT Computer. Prijateljske overture so bili deležni tudi Japonci, saj je bila sklenjena vrsta poslov z Nippon Steel, Nissan in Sumitomo Electric Industrial. Japonci lahko odslej kupujejo tudi IBMove mainframe s kloniranimi japonskimi operacijskimi sistemi. IBMova mreža zvez in koalicij je zdaj že tako kompleksna, da je ni mogoče več enostavno pregledati. Svetovna mreža preprodajalcev z dodano vrednostjo (VARS je kratica za value-added resellers) in tržnih partnerjev obsega že tisoče partnerjev in ge nara§ča. Seveda pa je IBHov najljubši partner še vedno uporabnik. IBMova značilnost je sposobnost podpore širokega spektra aplikacij vse do industrijskega knov;-howa. V prejšnjih letih je bila namreč ta ekspertiza zanemarjena zaradi okostenele birokracije in nekoristnih produktov, v letu 1988 je prišlo do obrata, in sicer v odnosih IBMa z njegovimi uporabniki in v njegovih produktih. IBHove operacije v ZDA so bile razceplene v pet poslovnih linij (prav za prav v šest, če se upošteva še obnovljena marketinška organizacija), vsaka z decentraliziranim odločanjem in produktno odgovornostjo. Tako si je IBM ponovno pridobil zgubljeni področji mainframov in mini-računalnikov. Njegov 103 MlPSni plus model z oznako 3090S je vrnil iBMu prvo mesto podjetja v železarski ligi. Toda model AS/400 je postal eden najuspešnejših produktov v novejši zgodovini IBMa, kot je izjavil John Akers; ta model je dobesedno zasvojil uporabnike. IBMova strategija vsakršnje rešitve je tako v povezani ponudbi stroja, podatkovne baze, aplikacije in uporabniške prijaznosti. Tako je IBM izdobavil kar 30000 teh sistemov v drugi polovici leta 1988 in realiziral višek več kot treh milijard dolarjev v šestih mesecih takorekoč iz nič. IBM naj bi ponovno osvojil tudi mišljenje uporabnikov na področju osebnih računalnikov. Na pohodu je večja pripravljenost, da se uveljavita iBMov operacijs)^i sistem OS/2 in mikro-kanalsko vodilo. Na potezi so tudi proizvajalci iz klonskega konzorcija. IBMovi posli v ZDA v primerjavi z lanskim letom niso bistveno napredovali zaradi forsiranja prodaje železnine namesto človeških zmogljivosti. Toda to se je v začetku letošnjega leta že spremenilo. Partnerstvo, popravljanje preteklih napak in izločanje obrobnih operacij so značilnosti IBMa v preteklem letu. Dobiček podjetja je narastel za zdravih 10,4% na 5,81 milijard dolarjev, prodaja pa se je povečala za 8% in se približala skupnim (okroglim) 60 milijardam dolarjev. A. P. Železnikar Digital Equipment v letu 1988 nost na vsakem koraku. Pred začetkom zmagovitega obdobja računalnikov VAX je obstajalo kar nekaj tekmecev DECa, ki so imeli hitrejše in zmogljivejše, tudi 32-bitne računalnike, v primerjavi z DECovo glavno usmeritvijo tipa PDP-11. Tako se je lahko razvilo podjetje Prime Computers na račun DECa, katerga prvi VAX se je pojavil nekaj let kasneje. Vendar v poslednjih letih spet oživlja spomin na vzpon DECa z njegovo VAX družino. V letu 1988 je DECa resneje zaskrbelo hitro napredovanje skupine mlajših podjetij. Vsa ta podjetja so nastala v osemdesetih letih in se hitro polastila trga delovnih postaj in programske opreme: Compaq Computer, Novell in Sun Microsystems. DEC pa se je zavedel svoje defen-zivnosti tudi v spopadu z IBMom. Čeprav Se vedno lahko vstopa na trg procesiranja transakcij in storitev sistemske integracije pa mora vendarle zavarovati osvojene pozicije v inčenirin-gu in sistemih delovnih skupin proti IBMu. Ti novi pojavi in tržne sile so primorale DEC, da temeljito revidira svoje načrte ene same računalniške arhitekture. Tako je DEC skupaj s podjetjema Mips Computer Systems in Tandy pripravil vrsto delovnih postaj z operacijskima sistemoma Unix in MS/DOS, da bi lahko konkuriral podjetjema Compaq in Sun. V razredu cenenih mrež tipa PC LAN pa naj bi se spopadel s podjetjem Novell. Še vedno pa DECov zamegljeni marketinški pogled ni povzročil zanikanja njegove usmeritve na področju komercialnih sistemov, tako da je DEC razkril proizvodnjo novih visoko zmogljivih računalnikov tipa VAX in programske opreme za procesiranje transakcij in s tem pritisnil na IBMovo usmeritev podatkovnih centrov. Zato je bil koncept VAXa izpopolnjen in razširjen v več smereh. Tako so nastale ločene računalniške družine za področja malih, srednjih in velikih računalniških sistemov. Kljub takim poslovnim potezam pa je bila prodaja serije VAX 8800 pod pričakovanji in DEC je iztržil doslej najnižji dobiček oziroma njegovo rast. Profit je znašal le borih 6% ali samo $l,21bn kljub 18% porastu prodaje. Izven-ameriška prodaja se je prvič povzpela na 52,4% . v celotnem letnem prihodku sl2,2B5bn. Glede na uspešnost poznih sedemdesetih let se je v letu 1988 prav gotovo pojavil vzrok za deja vu: DEC je razkril svoje načrte nove računalniške arhitekture, ki se imenuje Application Integration Architecture (AIA). Nosilec programskega okolja te arhitekture, ki je povezana z možnostmi heterogenega računanja in industrijskih standardov, je VAX. Pri tem je pomembno, da se z njo uvršča DEC v svet namiznega in značilno unixovskega pristopa svojih mlajših konkurentov. A. P. Železnikar Podjetje Digital Equipment Corp. (146 Main Street, Maynard, MA 01754) je v preteklem letu realiziralo prihodek 12 284 000 000 dolarjev, in sicer 48% v Severni Ameriki, 36% v Evropi, 15% v Aziji in na Pacifiku in 1% drugje. DEC ni več to, kar je bil v poznih sedemdesetih letih, namreč razburkano in samozavestno podjetje. Danes je DEC defenzivno podjetje, katerega vedenje razveljavlja njegovo obnašanje iz obdobja pred več kot desetimi leti. Ta opomba je prav gotovo aktualna tudi pri presojanju razmer, povezanih z domačo računalnišćko industrijo, za katero je prav gotovo značilna defenziv- Fujitsu v preteklem letu Japonsko podjetje Fujitsu Ltd. (Maronouchi Center Building, 6-1 Maronouchi 1-chome, Chiyoda-ku, Tokyo 100) je v preteklem letu realiziralo prihodek 10 999 100 000 dolarjev, in sicer 86% v Aziji in na Pacifiku, 10% v Severni Ameriki in 4% v Evropi. V preteklem letu je podjetje prekoračilo dva sistemska mejnika: pridobilo si je sloves najhitrejšega računalnika (le za kratek Cas) in sprejelo tržno odločitev . o spremembi ' sklepanja ■ sistemskih poslov. Pri tem se je predhodno oskrbelo še z ekspertizama podjetij Sun Microsystems in Amdahl o razvoju polprevodnikov in centralnih procesorjev. To sodelovanje z ameriškima partnerjema je omogočilo dobavo novih sistemov za japonski trg. Tako je Fujitsu lahko vstopil na hitro rastoči japonski trg inženirskih delovnih postaj z licenco Sun Microsystems za SPARC (tj. ris-covska Scalable Processor Architecture). Malo kasneje je Fujitsu uvedel na Japonskem Amdahlo-va sistema 5990-1400 in 5990-700. Ta dvojica, ki konkurira IBMovim mainframom ES/3 090, je Fujitsov prvi, ibmovsko programsko polno kompatibilni par mainframov. SPARCovska družina S delovnih postaj Fujitsa pomeni tudi prvi vstop podjetja v posle Unix inženirskih delovnih postaj . Ta plasma se. je na Japonskem povečal za 250% v letu 1988 in dosegel prodajo 70000 enot v primerjavi z 20000 enotami v letu 1987. Poslovna odločitev Fujitsa kaže na nove napore v smeri revitalizacije Fujitsove usmeritve na področje mainframov. Čeprav je prihodek iz računalniške dejavnosti podjetja narastel za 11,5% in dosegel vrednost ¥ 1,4 trilijone (sllbn), je bila ta rast manjša kot v prejšnjih dveh letih. Fujitsovo računalništvo je namreč doseglo nižjo raven prihodkov kot znaša ta raven za podjetje kot celoto. V decembru 1988 je Fujitsu začel prodajati osem modelov novo razvitih superračunalnikov serije FACOM VP 2000. Model VP 2600 zmore hitrost 4 GFLOPS (štiri milijarde operacij s plavajočo vejico v sekundi) vektorskega procesiranja. Vendar je bila najava te hitrosti kot največje na svetu le kratkotrajna, ker je NEC takoj za tem postavil na trg Se hitrejši računalnik. V vrsti mednarodnih kooperacij velja omeniti operacije Fujitsa, ki zadevajo glasovno in podatkovno komunikacijo v povezavi s podjetjem Business Communication Systems v Anaheimu v Kaliforniji. Ta operacija združuje razvoj, proizvodnjo, prodajo in storitve pod enotno organizacijo. Fujitsu je odprl tudi svoj novi tehnološki center za raziskave in razvoj in prikazal njegovo delo na razstavi Fujitsu Technology '88. Tu je Fujitsu pokazal tudi nevroračunalniške robote in sisteme umetne inteligence in sisteme za komunikacijo s koherentnimi svetlobnimi valovi, ki lahko multipleksirajo na tisoče slikovnih in milijone zvočnih signalov. Nadalje je pokazal fotonski preklopni sistem z obsegom 512 megabitov na sekundo, napredek v tehnologiji komponent vključno s 4-bitnim mikroprocesorjem, ki temelji na Josephsonovem spoju in tudi delovanje biosenzorja, ki je sestavljen iz biološke substance. A. P. Železnikar največji evropski domorodni oskrbovalec, ki je svoj računalniški izkupiček v letu 1988 povečal le za suha 2% v primerjavi s 7,7% v letu poprej. TO upadanje prihodka, razmehčanost evropskih poslov pisarniških sistemov in perspektiva enotnega evropskega trga po letu 1992 so v tradicionalno previdnem nemškem podjetju sprožili nove poslovne akcije. Tako je Siemens doživel svoj največji pretres na podrodu visokega managementa po letu 1969, da je lahko sprožil agresivno kampanjo ekspanzije v mednarodne operacije in v posodobitev svojega zastarelega svetovnega programa podpore svojih multinacionalnih računalniških partnerjev. Izjemi na področju novih produktov sta bili le prodaja delovnih postaj (osnovanih na SINIX) in laserski tiskalniki. Vendar se je bistveno izboljšala prodaja Siemensovih osebnih računalnikov, in sicer za probližno 50%. Tržno težišče je bilo v letu 1988 na sistemih Hicom PBX (to je bilo Siemensovo leto Hicoma) in se je tudi bogato izplačalo. Siemens je prodal 750 teh sistemov. Pridobivanje novih poslov, združevanje in skupni posli so dejavnosti, ki so se uvrstile visoko v program novega Siemensa. Njegov predsednik in glavni iavršilni uradnik Karlheinz Kaske je izjavil, "da bo upošteval vsakršnjo priložnost, ki se bo ponudila, če se bo ta vključevala v strateški koncept podjetja." To pa je seveda vse kaj drugega, kot smo vajeni' pri nas doma, kjer se pobuda duši, etiketira in omalovažuje. Kot del svoje ekspanzije je Siemens združil moči z londonskim elektronskim velikanom General Electric Co. (CEC) v novembru 1988 z namero, da si pridobi tudi britanskega komunikacijskega specialista Plessey Co. (PLC). To pa pomeni, da bo Siemens lahko izboljšal svoj položaj na dobro hranjenem britanskem elektronskem tržišču. V lanskem decembru pa je Siemens presenetil industrijo z najavo skupnih poslov z IBM na PBX področju, ki je bilo zgrajeno okoli IBMove podružnice Rolm, katero je IBM kupil v letu 1985. Siemens je pobral razvoj in proizvodnjo podjetja Rolm in si s tem podaljšal svojo tržno roko v ZDA, hkrati pa dosegel, da bo IBM njegov Hicom sistem prodajal skupaj z računalniško opremo v Evropi. Drugi skupni posli Siemensa v preteklem letu zadevajo Intel, s skupno kreacijo novega podjetja BiiN v Hilboro, Oregon. To podjetje bo razvijalo misijsko kritične sisteme v ZDA in v Zapadni Nemčiji. V okviru svojega prestrukturiranja je Siemens začel menjavati delovna mesta tisočim svojih uslužbencev skladno z novo filozofijo podjetja, ki predvideva 15 do 20 prožnih in neodvisnih poslovnih skupin. Medtem pa je Siemens zmanjšal tudi svojo delovno silo za 6000 delavcev v Nemčiji. A. P. Železnikar Siemens v letu 1988 Prestrukturiranje podjetja Olivetti glede na novo realnost Zapadno nemško podjetje Siemens AG (Wittelsbacherplatz 2, D8000 Muenchen 1) je v preteklem letu realiziralo prihodek 5 951 000 000 dolarjev, in sicer 89% v Evropi, 10% v Severni Ameriki in 1% v Aziji in na Pacifiku. Siemens je Podjetje Olivetti (Via G. Jervis 77, 10015 Ivrea, Italija) se je preoblikovalo s ciljem, da ohrani svojo donosnost in da se pripravi za leto 1992. S svojim visokim devetim mestom, takoj za nemškim Siemensom, je podjetje v preteklem letu realiziralo prihodek 5 427 900 000 dolarjev, s plasmajem 81% v Evropi, 10% v Severni Ameriki, 6% v Aziji in na Pacifiku in 3% drugje. Stisnjeno v ožajoSe pogoje, spodbujeno s trenutno donosnostjo in ujeto v tržne situacije, ki postajajo Čedalje bolj specifične, je italijansko podjetje Ing. C. Olivetti & Co. SpA v letu 1988 napovedalo, da je sprožilo masivni program prestrukturiranja. V povezavi s to reorganizacijo podjetja je bil odpoklican iz ZDA Vittorio Cassoni, ki ga je Olivetti posodil podjetju AT&T za vodenje njegove divizije podat-' kovnih sistemov (od novembra 1986). Tako je Cassoni postal soupravljavski direktor predsednika podjetja Carla de Benedettija. Da bi lahko konkuriral podjetju Pacific Basin in Japoncem, je Olivetti ustanovil novo divizijo Olivetti Office za produkte giroke potroSnje, kot so pisalni stroji, tekstovni procesorji in naprave za faksimile in kopiranje . Olivettijeva sistemska in mrežna skupina se je spopadla z' Digitalom, IBMom, NCRom in drugimi na podroSju aplikacijskih rešitev, ki zadevajo porazdeljeno procesiranje podatkov. Pro-duktna linija skupine obsega široko področje PCjev in sistemov z delovnimi postajami, mini-jev, mrež in Hitachijevih mainframov, ki so IBMovsko kompatibilni, in sicer za italijansko in špansko tržišče. Olivettijeve informacijske storitve so bile oblikovane za dejavnosti sistemske integriraci-je in storitev in naj bi konkurirale podjetjem, kot so Electronics Data Systems Corp. in francoski Cap Gemini Sogeti. Motivacija za pregrupiranje Olivettija je bilo poslabševanje profitnosti med letom, ki je upadla na koncu leta na 11,5% oziroma na 356 milijard italijanskih lir ($273,4m). Prihodki podjetja v celoti so narasli za 14% na It lir 8 407 milijard (s6,5bn), pri tem so računalniški dohodki narasli za 17%. Dobiček je v preteklem letu upadel za 30%. Kljub temu so vsa produktna področja izkazovala naraščanje. Olivetti je imel težave pri gradnji svoje minira-čunalniške prodaje, kljub veliki izbiri produktov, vključno s svojo lastno LSX linijo, AT&T 3B sistemi in sistemi, občutljivimi na napake podjetja Stratus Computer Inc. Prodaja minira-čunalnikov se je povečala le za 2%, tj. na vrednost s614m. Olivetti si je v letu 1988 prizadeval za integracijo svojih produktov s sistemi drugih proizvajalcev, ki so del njegove OSA (Open System Architecture). Olivetti in Digital sta se sporazumela za izmenjavo tehnologije, ki omogoča integracijo Olivettijevih PCjev v Digitalove mreže z uporabo DECovega NAS (Network Application Support). Povezava z DECom se je tako bistveno okrepila, letos pa je temu sledil Se sporazum, da bo Olivetti oskrboval DECa s PCj i na evropskem tržišču. Olivettijeva skupina za sisteme in mreže je predstavila novo serijo PCjev P500 in P800, ki uporabljata Intelov procesor 386SX in IBMovo MicroChannel arhitekturo. Olivetti in ameriški Stratus sta se dogovorila za razvoj na napake občutljivega operacijskega sistema Unix za Stratusove, na napake občutljive računalnike, tako da bodo ti kompatibilni z Olivettijevirai sistemi. Olivetti ima za seboj dolgo zgodovino investiranja v mala tehnološka podjetja širom po svetu. V svojem portfolio ima trenutno 240 podjetij, vključno z Acorn Computers v Britaniji, .Bunker Eamo v ZDA, skandinavskim Scanvest-Ring in Triumph Adler v Zapadni Nemčiji. Glavna naloga Cassonija je, da poveže te ločene elemente in oblikuje koordinirane produktne linije skozi podjetje. Novo prestrukturiranje podjetja in poudarek na OSA naj bi olajšala izvedbo te naloge. Cassoni pa mora upoštevati predvsem hitre spremembe na evropskem trgu PCjev, čedalje večje oddaljevanje podjetja ATStT od Olivettija in njegovo odločitev, da si poišče dobavitelja PCjev v ZDA. Seveda pa se približuje tudi leto 1992. To pa pomeni Se kaj več kot je lahko notranje prestrukturiranje podjetja, ko mora biti to usmerjeno v unificirani evropski trg. Ta izziv pomeni prestrukturiranje celotne industrije. Cassoni dodaja k temu še, da je podobnih podjetij enostavno preveč. A. P. Železnikar Francoski Croupe Bull v letu 1988 Francosko računalniško podjetje Croupe Bull (121 Avenue de Malakoff, 75116 Paris) je v letu 1988 realiziralo prihodek 5 296 700 000 dolarjev, in sicer 59% v Evropi, 40% v Severni Ameriki in 1% v Aziji oziroma na Pacifiku. V francoskem podjetju Croupe Bull ima francoska vlada 92% holding. V preteklem letu je to. podjetje realiziralo trdno kontrolo z globalno posestjo podjetja Honeywell Inc. Rezultat tega je, da je eno prvih ameriških ra'čunalniških podjetij v lasti francoskega ljudstva. Buli je povečal svoj delež v ameriški podružnici Honeywell Bull Inc. iz prejšnjih 42,5% na 65,1% v letu 1988, znižal Honeywellov delež na 19,9% in pustil nespremenjen delež NECa na 15%. AmeriSko podjetje je preimenoval v Buli HN Information Systems Inc. S tem je Buli lahko najavil svoj svetovno konsolidirani prihodek z vrednostjo FF 31,5 milijard (s5296,7m). Francoski del v tem prihodku ni bil večji od 39,9%. Strategija Bulla v naslednjih letih ni v visoki donosnosti, temveč v povečevanju prihodka, čeprav se je njegova donosnost v letu 1988 povečala tako v Evropi kot v Ameriki. Pomemben nov produkt Bulla v letu 1988 je prav gotovo poslovni sistem DPS 9000, ki ga poganja operacijski sistem GCOS 8. Buli je najavil tudi mali poslovni sistem DPS 4000 in izboljšavo popularnega departmentnega sistema DPS 7000. Vstopil je tudi v področje odprte sistemske mreže z desetimi Unix sistemi, vključno z DPX 1000, 2000, 3000 in 5000, ki so bili razviti v Franciji. V začetku leta 1989 si je Buli kot prvi na svetu pridobil pravico do uporabe paketa X/Open v svoji verziji SPIX Unixa System V.3. Na spodnjem koncu svoje procesorske ponudbe je Buli razširil svojo družino delovnih postaj Questar in uvedel svoj OS/2 mikrosistem, imenovan Micral 75. Prodaja obeh produktnih linij je v zadnjem letu izredno narasla. A. P. Železnikar Kovanje denarja z delovnimi postajami ali Sun Microsystems v letu 1988 Blesk podjetja Sun Microsystems se skriva v agresivnem določanju cen in visokih zmogljivostih njegovih produktov. Sun Microsystems Inc. (2550 Garcia Avenue, Mountain View, CA 94043) je reraliziralo 1 461 600 000 dolarjev v letu 1988, in sicer 60% v Severni Ameriki, 24% v Evropi in 16% v Aziji in na Pacifiku. Ko bo zares nastopila doba odprtih sistemov, bodo proizvajalci informacijske tehnologije soočeni z igro novih pravil. Ko bodo uporabniki že zamreženi v specifičen hardware in software, bodo proizvajalci lahko pospeševali le še inovacijo in sprejemali nižjo profitno stopnjo, če bodo želeli ostati v teloni s trgom. Izgleda, da se vsaj eden od proizvajalcev obnaša tako, kot da je nova realnost odprtih sistemov že pred nami. Podjetje Sun Microsystems je združilo vratolomno hitrost uvajanja novih produktov z agresivnim določanjem cene, z uresničevanjem odprtih sistemov in s tem, kar je bilo poimenovano kot mrežno računalništvo. Posledica tega je bila osupljiva rast. V pičlih sedmih letih je Sun vzcvetel v milijardno podjetje ($l,4616bn) in postal zvezda na trgu delovnih postaj, vrednem $4,lbn. Samo v letu 1988 se je prihodek Suna povečal za 93,4%, profit pa za 86,7%, ko je dosegel vrednost s89,6in. Na koncu leta 1988 je imel Sun v zakupu že 28,3% svetovnega trga delovnih postaj, tj. za 4,2% več kot v letu 1987. Ta tržni delež je Sun odvzel svojim tekmecem, in sicer podjetju Apollo Computer, katerega delež je padel za 4% na 13,5% celotnega tržnega deleža in IBMu, ki je obdržal le še 2,6% trga. Tako je porinil Apollo v naročje Hewlett-Packarda v začetku tega leta. Sunu je uspelo znižati zapreke v postavljanju cene in zviševanju zmogljivosti ter z vnov-čevanjem na zahtevo tehničnih uporabnikov in z naraščanjem Števila komercialnih uporabnikov. Podobno kot osebni računalniki nudijo tudi Su-nove delovne postaje podporo za vežopravilnost (multitasking) in večuporabnost, vključno z dostopom v skupne zbirke, visoko resolucijo, hitro grafiko itd. S temi lastnostmi so Sunovi produkti postali prvaki na področju programskega iženiringa in oblikovalne avtomatizacije. Ta trčni segment je pokril 68% Sunovih uporabnikov v letu 198B. Kasneje pa so Sunove delovne postaje postale popularne tudi med manj-tehničnimi uporabniki, kot so varnostna in izdajateljska podjetja. Koncept distribuiranega, mrežnega računalništva z uporabo delovnih postaj in storilnikov (servers) je osvojil domišljijo uporabnikov Fortune 2000. T.i. namizna revolucija, ki se je začela s PCji v letu 1980, je dozorela v zahtevi po moči in odprtosti sistema v obliki zamreženih (v mrežo povezanih) delovnih postaj. V prepričanju, da so delovne postaje naslednja etapa v namizni revoluciji, je Sun v poslednjih letih agresivno povečeval njihovo moč ob istočasnem zniževanju njihove cene do ravni osebnih računalnikov. Sun, ki je v letu 1988 uvedel delovne postaje s svojim RISC procesorjem (SPARC), je to arhitekturo dobro izkoristil. Pri tem je uvedel spodnjo verzijo s 7 milijoni ukazov na sekundo (MIPS) svoje sparcov-ske produktne linije Sun 4 z osnovno ceno $19950. Zgodaj v tem letu se je pojavila 12,5- mipsna verzije z osnovno ceno $8995. Letos naj bi Sun plasiral 90000 sparcovskih delovnih' postaj . Očitno bo Sun nadaljeval s svojim načinom odprtih sistemov in s strategijo agresivnih novih produktov in postavljanja cene. V letu 1988 je namenil Sun 13% prihodka raziskavam in razvoju. Tudi letos bo Sun namenjal R&D podoben delež, ki je nad industrijskim povprečjem (9,9%). Sunovo agresivno postavljanje cen je dopuščalo nizko operativno maržo (mejo rentabilnosti), ki je znašala 10%. A. P. Železnikar Finska Nokia na pohodu Finska Nokia Corp. (P.O.Box 226, 00101 Helsinki), 50. računalniško podjetje v svetovni razvrstitvi, je v računalništvu realiziralo prihodek 1 165 100 000 dolarjev, predvsem z združitvijo stagnirajoče švedske podatkovno sistemske divizije z hitro rastočo finsko podružnico v enotno, dinamično in učinkovito evropsko podjetje. Prav to je uspelo njenemu briskantne-mu in ambicioznemu predsedniku (Kalle Isokal-lio). Nokia je rezultat združitve med Data Division of Ericson Information Systems, ki je podružnica velikega skandinavskega telekomunikacijskega podjetja LM Ericson in računalniških prodajnih operacij finskega industrijskega konglomerata Nokia. Ericson je obdržal le 20% delež, Nokia pa odločujoči vpliv. Združitev je katapultirala prihodek Nokia Data za 166%, pri tem je profit narastél le za suhih 11,3%, vendar se je združitev Nokie pokazala kot skupinska profitnost v konglomeratu. Nova Nokia Data prodaja predvsem terminale, PCje, delovne postaje in sisteme za skupinsko delo. Tako je bilo instaliranih vež kot 700 000 profesionalnih delovnih postaj. Digital in IBM kupujeta njene terminale in prodajne monitorje za evropsko tržišče. Na Finskem distribuira Nokia tudi sisteme DPS 8 in DPS 6 francoske Croupe Bull, na napake občutljive računalnike podjetja Tandem in nekatere z IBM kompatibilne mainframe podjetja National Advanced Systems. Uporabniška baza podjetja Nokia Data obsega bančništvo, zavarovalništvo, prodajno in javno administracijo. Zunaj Skandinavije sta njena uporabnika nemška Bundespost in britanska Midland Bank. Eden od vzrokov za nakup Erics-sonovih operacij je bila prav uporabniška baza. Produktni razvoj Nokie je pogojen s kombinacijo mreženja in ergonomije. S stališča uporabnika to ni svet OS/2 ali Unixa, temveč svet lokalne mreže, zatrjuje Isokallio. Oblikujemo sisteme, ki povečujejo uporabnost mrež s priključevanjem okolij OS/2 in Unix. Različni bomo v uporabnosti terminalov in sistemov z delovnimi postajami in to ne le na ravni radijske emisije in fizične in softwarske ergonomije, pravi Isokallio. A. P. Železnikar novice in zanimivosti news Zakaj se inženirji zavzemamo za tehnološko tržno združevanje Vedno pogosteje imamo priložnost, da preko dnevnega časopisja zvemo o krovnih ali "holding" podjetjih. Bistvo teh je povezovanje s pomoSjo ustanovitve krovnega podjetja, kamor se prenese poslovni sklad. Krovno podjetje pa nato prenese ta kapital nazaj na matiCna podjetja. Na ta način bi družbena lastnina dobila svojega lastnika. Mnogo je tudi govora o zdravem načinu poslovnih vezi med podjetji. Ideja je na prvi pogled imenitna, samo da se ne ve, na kakšen način se podjetja združujejo. Se manj pa na kakšen način in kaj se proizvaja. Načinov združevanja je več glede na motiv združevanja. Najpogostejša je povezanost s tržnim motivom. Tako imenovana tržna proizvodna povezanost je po mojem mnenju enorazsežna in nepopolna, ker ne pove ničesar o notranjih tehnoloških pogojih za nastop na trgu. Vsi mediji pritrjujejo, da so potrebni ekonomisti, ki znajo izračunati in upravljati s profitom, zato je motiv tržni. Da je poleg tega proizvodni, je vsakomur jasno, ker morajo profit delavci proizvesti. Nihče pa si iz prastrahu pred inženirji ne upa niti omenjati, da je vsaka proizvodnja plod izumljanja, to pa je delo inženirjev (iz fr. Ingenieur = izumitelj in lat. ingenium = izum). Imamo lahko Se tako popolne tržno proizvodne modele, vendar brez inženirskega, ki izumlja in tehnološkega dela, ki zna izum prenesti v proizvodnjo in naučiti delavce proizvajanja, nimamo ničesar tržiti, še manj pa profitirati. Inženirju ni mogoče ukazati nek izum, ker je kreativnost obratno sorazmerna s stopnjo represivnosti, pač pa mu je potrebno nuditi pogoje za izumljanje, kot so laboratorijska in informacijska sredstva. Inženirju je potrebno pustiti "liberte creatrice" seveda z nekim rokom, v katerem se lahko seznanja z novostmi na svojem področju in neovirano eksperimentira. Po tem času mora imeti proizvod, ki je laboratorijsko preizkušen in pripravljen za tehnologijo in proizvodnjo. Šele potem lahko nastopa podjetje s proizvodom, ki je rezultat znanja, na konkurenčnem trgu. Popolnejša od tržno proizvodne je tehnološko tržna povezanost. Tehnologija (iz gr. techne = spretnost, logos = razum) pove, na kakšen način proizvajati izume inšenirjev, trg pa ne določa proizvodnje, pač pa na izoblikovano proizvodnjo samo zahteva količino. Sodeč po literaturi, je tehnološko tržna povezanost osnovana na načelu, da mora biti vsako podjetje profitno, ali pa mora slediti profitnemu podjetju. Podjetje, ki ni profitno, ni nujno tudi nekoristno, ker ga potrebujejo profitna podjetja za svoj tehnološki proces. Lahko pa je nasproti temu neko podjetje profitno, vendar nekoristno za združitev, ker kupuje proizvode za združitev nekoristnih podjetij. Dejstvo, ali je neko podjetje profitno, je določeno s tehnološkim faktorjem q(i,j). To je vrednost proizvoda podjetja j, ki ga mora podjetje i od njega kupiti, da proizvede enoto vrednosti {npr. Is). Tehnološki faktor je vedno manjši od 1, Se več, če je podjetje profitno, potem mora biti tudi vsota tehnoloških faktorjev manjša od 1. Predpostavimo, 6 podjetij v medsebojnem tehnološko tržnem odnosu. Naj matrika Q predstavlja tehnološko matriko združitve podjetij: "l/2 0 1/4 0 O O 1/4 1/4 1/4 0 O O 1/2 0 1/2 0 O O 0 0 0 1/4 3/4 O 0 0 0 1 0 0 O 1/4 O 1/4 O 1/4 Vsaka vrstica vsebuje tehnološke faktorje enega podjetja. Na prvi pogled lahko ugotovimo, da so profitna podjetja 1,2 in 6. Vsa druga so neprofitna, ker imajo vsoto vrstice enako 1. Predpostavimo zdaj, da podjetja svoj presežek shranjujejo preko krovnega podjetja v banko. Zato se matriki Q doda Se en stolpec, ki določa, koliko profita posamezna podjetja prispevajo. Vrednosti tega stolpca so enake preostanku vsote vrstice do 1. Dobimo verjetnostno matriko P, ki določa najbolj verjeten tehnološki odnos med podjetji vključno s krovnim podjetjem P(0): P(0) P(l) P(2) P(3) P(4) P(5) P(6) P = Zdaj lahko ugotovimom koristnost podjetij. Krovno podjetje ne proizvaja, zato ima vse tehnološke faktorje razen prvega enake 0. Prvi faktor je absorbirajoč, ker mora vsota vsake vrstice biti enaka 1 in ker so vsi drugi členi nič, mora biti prvi 1. Stolpci matrike nam kažejo tržni odnos, vrednosti členov matrike pa tehnološki, odnos. Takoj lahko ugotovimo, da imata podjetji 1 in 3 enak tržni odnos, eno od drugega kupujeta. Zato ju lahko združimo. Faktorji podjetij 4 in 5 so ergodični, neodvisni od drugih, zato podjetji združimo. če je v presečišču vrstice i in stolpca j neka vrednost, to pomeni da podjetje j proizvaja za podjetje i, tako da podjetje j koristi podjetju i. Po tem principu narišemo diagram stanj sistema. Pričnemo s podjetjem P(0), ki ne proizvaja, pač pa upravlja s podjetji. Podjetje 1 je profitno in posredno preko njega tudi podjetje 3. Podjetje 2 je prav tako profitno in koristno podjetju 1 in 3. Koristno podjetju 2 je tudi podjetje 6, vendar to podpira podjetji 4 in 5, ki pa nista profitni. Zato se združijo samo podjetja 1,2 in 3 preko krovnega podjetja, druga pa se v tej združitvi opustijo. Smer puščic določa tehnološko pogojen pretok denarja. P(0) P(1),P(3) P(2) P(6) ^ P(4),P(5) Nova, tehnološko tržna matrika je potem: P(0) P(l) P(2) P(3) 1 0 0 0 0 0 0 P(0) 1/4 1/2 0 1/4 0 0 0 P(l) 1/4 1/4 1/4 1/4 0 0 0 P(2) 0 1/2 0 1/2 0 0 0 P(3) 0 0 0 0 1/4 3/4 0 P(4) 0 0 0 0 1 0 0 P(5) 1/4 0 1/4 0 1/4 0 1/4 P(6) P = 10 0 0 1/4 1/2 O 1/4 1/4 1/4 1/4 1/4 O 1/2 O 1/2 P{0) P(l) P(2) P(3) Stanje krovnega podjetja je absorbirajoče in iz matrike Q dobimo novo matriko N = 1/(1 - Q), kjer je I enotina matrika. Matrika N določa proizvodnjo v stolpcu, ki jo stimulira enotino naročilo v vrstici. Tako nam proizvodni faktor n(i,j) določa vrednost proizvodnje podjetja j, ki ga stimulira enota vrednosti (1$) naročil na podjetje i. Matrika V sumira vrednost proizvodnje po podjetjih (vrsticah i); N = 4 O 2 8/3 4/3 2 4 0 4 V = Tako nam naročilo 1$ na podjetje 2 stimulira proizvodnjo 8/3$ od P(l), 4/3$ od P(2) in 2$ od P(3). Na to naročilo napravi P(l) profit 8/3 x 1/4 = 2/3, P(2) profit 4/3 x 1/4 = 1/3 in P(3) profit 2x0=0, ker je P(3) neprofitno, skupaj tako podjetje 2 napravi 1$ profita. Trg nastopa na začetku, ker z analizo trga ugotovimo njegovo kvaliteto in na koncu, ko določa kvantiteto tehnološkega procesa. Na zahteve trga se podjetja odzivajo preko vrstičnega vektorja T, ki pove količino dolarskih naročil za podjetja, n.pr.: T = (1,3,2) Na tako zahtevo trga dobimo s produktom T x N = (20,4,16) proizvodnjo, ki jo ustvarijo posamezna podjetja. Totalna proizvodnja je določena s produktom T x V = 40$. V tej proizvodnji napravi P(2) 3$ profita. Podobno izračunamo profit še za drugi dve podjetji. Dejstvo, da je podjetje lahko koristno tudi, če je neprofitno, potrjuje začetno tezo, da mora podjetje v tehnološko tržnem razmerju biti ali profitno, ali pa mora slediti profitnemu podjetju. Celoten proces ima po mojem mnenju izvor v inženirskem delu, ker sam trg in proizvodnja brez izumiteljskega in tehnološkega deleža ne zadoščata za profit podjetij. Literatura: J.G.Kemeny, J.L.Sneli, "Finite Markov Chains", Springer Verlag, N.Y., Heidelberg, Berlin, 1976. Rihard Piskar Na rob konferenci o zanes^ivosti in kvaliteti Na mednarodni konferenci, ki jo organizira lASTED (International Association of Science and Technology for Development) v Luganu,, Švica, od 20. do 22. 6. 1989, je bilo med 72 prispevki svetovnih ekspertov v treh dneh mogoče slišati in videti tudi dva referata Iskre Delte, enega v sodelovanju s Fakulteto za elektrotehniko in računalništvo iz Ljubljane. Prvi je bil "Zanesljivostna napoved ahitekture hiperkocke PARSYS" in drugi "Razpolož1j ivostno analitično orodje za kompleksne sisteme", ki sta poleg prodorne tematike paralelnega procesiranja in zanesljivostnega.inženirstva predstavila širši javnosti del razvojnih dosežkov Iskre Delte. Sodoben razvoj računalništva v svetu gre v dve smeri: superračunalnikov in paralelnih računalnikov. Prvi imajo poudarek na tehnologiji zelo visoke stopnje integracije in distribuiranem procesiranju, ki je kvaziparalelno, drugi pa poleg visoke tehnologije temeljijo na čistem paralelizmu. Bistvo paralelizma je v tem, da ni več sukcesivnega izvajanja nalog, pač pa se vsaka naloga razbije na množico podnalog in se vsaka od njih istočasno in sinhrono izvaja. S tem se pridobi na hitrosti, ki je pomembna predvsem pri reševanju problemov, ki zahtevajo veliko obdelav v kratkem času, poleg tega pa na napakovni tolerantnosti, ki dopuSča, da kak procesor ali del pomnilnika celo odpove, vendar pa drug procesor prevzeime njegovo nalogo. Tak sistem Je PARSYS, paralelni sistem Iskre Delte v raziskovalno razvojni fazi. Posebno živahna diskusija se je razvila po predstavitvi analitičnega večrazsežnega sistema super-kub, za numerične evalvacije razpoložljivosti hierarhičnih, distribuiranih in paralelnih sistemov, ki deluje na sistemih Delta VMS in ga Delta s pridom uporablja. Bazira na večrazsežnostnih naključnih sistemih, ki prostorsko ponazarjajo stanja sistema, ki ga analiziramo in jih ovrednoti numeriCno, kar je nadvse pomembno pri prognozi obnašanja sistema v spreminjajočem se okolju. Sistem je interaktiven, trenutno je v fazi prenosa na sisteme Delta PC. Sodeč po ugotovitvah s konference zanesljivost in kvaliteta nista sinonima. Zanesljivost, kot Širši pojem, je često nepravilno uporabljen v konceptu kvalitete. Lahko se diskutira o tem, da je kvaliteta statični in zanesljivost dinamični deskriptor nekega procesa ali izdelka. Izložbeni izdelek je lahko visoko kvaliteten, toda njegova zanesljivost je izmerljiva samo z rabo, ali pa je ocenij iva s prognozo. Gledano na drug način je njegova kvaliteta'intrinsična ali inherentna na izdelek sam, medtem ko je zanesljivost merilo njegovih performans v sistemu in določenem okolju. Zanesljivostni pristop k problemu zadovoljstva kupca je posledica kombiniranega razvoja kvalitete in zanesljivosti. Znano je, da so Japonci pred 15 leti dobivali instrukcije o kontroli kvalitete iz ZDA. Dobili so model in uporabljali so ga. Toda ne samo, da so ga uporabljali, tudi izboljšali so ga. Večina vseh metod kontrole kvalitete od motivacij ljudi, zero defektov, treniranju osebja iz principov kontrole kvalitete se je pričelo v ZDA. Danes se v ZDA že učijo od Japoncev in se zavedajo bazične pomembnosti zanesljivosti in kvalitete za podjetja in njihov vpliv na tržiSče in poslovno strategijo v področju razvoja, strokovni spretnosti in pogodbenem odnosu s kupci. Na drugi strani malo Japoncev spodbija vodilen vpliv ameriških inženirjev na področju zanesljivostnega inženirstva, prav tako kot priznavajo ameriško vodstvo v sodobnem razvoju in tehnologiji, čeprav Japonci izvrstno upravljajo proizvodnjo in marketing visoke kvalitete predvsem za potrošniške izdelke, je tehnologija za temi produkti dobro znana. Prav tako Je zelo malo japonskih projektov, ki zahtevajo visoko zanesljivost kot jo zahteva vesoljski raziskovalni program. Japonski cilj je osvojiti zanesljivostno teorijo, razvoj in inženirstvo. Medtem pa je jasno, da zna predstavljati tradicija Japoncev, ki zavira razvoj individualnih dosežkov in spoznanj v korist timskega dela, zanje težavo, da bi se istovetili z njimi nasprotno ameriško tehnološko kreativnostjo. Na vprašanje, kakšen model razvoja zanesljivosti in kvalitete uporabiti v Jugoslaviji, menim, da nikakor ni priporočljivo, da spoznamo vse faze razvoja, kot ZDA ali Japonska, pač pa se lahko na razvoju teh dveh naučimo in nadaljujemo pri njunih izkušnjah. Jugoslovanska svobodnost mišljenja in kreativnost, ki Je bližja ameriškemu načinu, nam daje misliti, da nasilno usmerjanje v japonski model ne bo prineslo zaželjeni učinek. Zato je predvsem v sorazmerno začetni fazi razvoja zanesljivostneg* Inženirstva in kvalitete zelo pomembno sprostiti kreativni potencial, ki ga imamo in ne podrediti individualnih dosežkov skupnim. ciljem. Vkolikor bi že na zagetku doloSili okvire, v katerih se lahko razvija zanesljivostno inSenirstvo kot del aktivnosti kontrole kvalitete, kot kažejo težnje v nekaterih okoljih, bi hkrati zadu§ili kreativno mišljenje, brez katerega razvoj ni mogo£. Tudi na priSujoCi konferenci je bilo 6 referatov jugoslovanskih, ki dokazujejo jugoslovansko kreativnost v razvoju konceptov zanesljivosti in kvalitete sodobnih tehnoloSkih dosežkov. Rihard Piskar Informacyska tehnolog^a v Španci špansko gospodarstvo je v razcvetu in celotno področje informacijske tehnologije raste nezadržno z ekonomskim napredovanjem podjetij. Čeprav na Španskem trgu podjetje IBM Se vedno usmerja tržne potrebe pa vrsta tujih proizvajalcev sodeluje v Španskem razcvetu. Španija je dolgo samevala na slepem koncu Evrope, odkar so njeni konkvistadorji osvojili Latinsko Ameriko. Naenkrat pa je v zadnjih nekaj letih postala gospodarsko najprivlačnej§a dežela. Njena brsteSa ekonomija je uravnotežena med prednosti podrazvitosti - cenenim delom in neizkoriščenim . kapitalom - in prednostmi, ki izvirajo iz Članstva v Evropski skupnosti. Rastoča španska ekonomija vleče s seboj tudi informacijsko tehnologijo; obe sta posledica naraščajočega bogastva in sposobnostne tehnologije, ki omogoča ekonomsko ekspanzijo. V zadnjih petih letih je računalniška prodaja v Španiji narasla za 321%, in sicer prek 4 milijarde dolarjev. Proizvodnja računalniške industrije se je povečala za 335%, in sicer na približno 1 milijardo dolarjev. Prodaja računalniške aparaturne opreme je pokrila 60% trga, vzdrževanje, šolanje in svetovanje približno 21%, programska oprema pa približno 17% trga. Vsa tri področja izkazujejo letno povečevanje dohodka med 20% in 30%. Se posebej so narastle potrebe po osebnih računalnikih. Leta 1985 je le 2,5% poslovodnih delavcev uporabljalo osebne računalnike. V letu 1987 jih je bilo že 6%, v letu 1992 pa naj bi dosegli razmerje 32%. V tem deviškem prodajnem okolju ni več presenetljivo, da je Španija postala privlačna za tuje investitorje. Manj kot 7% španskega industrijskega dohodka izvira iz čistih domačih (domorodnih) podjetij. Od leta 1983 se je uvoz povečal za 327%, in sicer na vrednost 3,404 milijarde dolarjev - štiri od petih prodanih osebnih računalnikov v Španiji so uvoženi. V Španiji je kar nekaj muLtinacionalk, ki nimajo svojih podružnic ali distribucijskih zastopnikov. Podjetja za proizvodnjo in sestavljanje v Španiji so npr. Hewlett-Packard, ki izgrajuje v svojem glavnem središču za periferijo novo tovarno, razSirja pa tudi svojo tovarno v Barceloni; tudi proizvodnja tiskalnikov in avtomatičnih blagajn podjetja Fujitsu se je povečala za 35% in 75% v zadnjem letu. Podjetje Fujitsu-Espana proizvaja v svoji tovarni v Malagi tudi miniračunalnike, mikroračunalnike in naprave za pisarniško avtomatizacijo; v to tovarno je podjetje investiralo v zadnjem letu nadaljnjih 10,5 milijonov dolarjev. Podjetje Fujitsu ima svoj glavni evropski urad v Madridu in njegova španska podružnica Fujitsu-Espana je zelo uspešna. Podjetje se je usidralo v Španiji pred 15 leti in je začelo skupni posel s španskim računalniškim proizvajalcem Secoinsa, in sicer z proizvodnjo v Španiji konstruiranega računalnika. V letu 1986 je španska PTT Telefonica odkupila 40% delež. Podjetje Fujitsu-Espana je pridelalo v razdobju 1987/88 dobiček 7,6 milijona dolarjev pri dohodku 160 milijonov dolarjev, kar je pomenilo povečanje dobička za 27%; dobiček naj bi se v tem letu povečal še za 50%. Kljub uspešnosti Fujitsu-Espana v Španiji pa je podjetje IBM še vedno prevladujoče na španskem računalniškem trgu. Na IBM odpade kar 36% celotne industrije, in sicer kot na dobavitelja računalnikov in izvoznika. Njemu sledita Philips kot proizvajalec terminalov in Epson kot prizvajalec tiskalnikov. Druge multinacionalke s pomembnimi deleži v Španiji so še Unisys, Olivetti, Nixdorf, Xerox, DEC in NCR. Na eksplozivnem trgu osebnih računalnikov je značilno prodrlo podjetje Tünstrad z modeloma 1512 In 1640 in podjetje Altos, ki je izdobavilo 5000 večuporabniSkih mikroračunalnikov v zadnjih šestih letih. Na veliko večjem francoskem trgu je Altos prodal samo 10000 sistemov v 10 letih. Altos napoveduje, da bo po letu 1992 naraščal španski trg za večuporabniSke sisteme hitreje kot v katerikoli drugi evropski državi-. Vstop podjetja ICL na špansko prizoriSCe sega 10 let nazaj, ko je bilo odkupljeno Sin-gerjevo mednarodno računalniško podjetje na podedovanem španskem tržišču. Konec lanskega leta pa je ICL oblikoval skupni posel (joint venture) z andaluzijskim razvojnim institutom, da bi razvijal programsko opremo in storitve, namenjene zdravstvenim, izobraževalnim, storitvenim in javnim ustanovam. Drugi, vertikalni tržni interes icLa v Španiji je trgovina na drobno. Skupni posel podjetja ICL-Sistemas obvladuje iz Sevilje le 30 inženirjev in tehnikov. ICL vzpostavlja tudi mednarodni nakupni urad v Barceloni, ki bo preizkušal španske izdelke glede na njihovo ustreznost za izvoz v ICLove tovarne kjerkoli. ICL bo oblikoval tudi reprezentativno središče v Madridu, kjer bo razvijal in prodajal aparatumo in progreunoko opremo po vertikali španskim vladnim ustanovam. Španija postaja eno najpomembnejših razvijajočih se področij Ev^pe. Tako se razvijajo tudi številne računalniške svetovalne organizacije v Madridu, Barceloni in Sevilji, skupni izobraževalni center pa je Segoviji. Čeprav tudi na španskem trgu domiriirajo multinacionalke, kažejo španska podjetja za informacijsko tehnologijo veliko zagnanost in ustvarjalnost. Investronica je španski pionir na področju osebnih računalnikov in obvladuje 30% tržišča z 250000 instaliranimi enotami. To podjetje je bilo ustanovljeno pred devetimi leti kot tehnični oddelek tekstilne industrije Induyco, ki je sedaj član grupacije El Corte Ingles. Tako je Investronica lahko izkoristila aplikativne niše v računalniško podprtem oblikovanju in proizvodnji tekstilne industrije, ko je izvažala sisteme z delovno postajo v 30 držav. Vodilno špansko podjetje za programsko opremo je Centro de Calculo de Sabadell (CCS), Xi je nastalo pred 25 leti, vendar je v letu 1972 postalo vodilno špansko podjetje za razvoj teleprocesorske mreže. 75% podjetja je v francoski lasti, sodelovalo pa je v različnih raziskovalnih projektih v Evropi, vključno v projektu Esprit. Podjetje prodaja npr. Masterpat, ki je progrfimski paket za upravljanje patoloških primerkov in npr. tudi pogodbo za računalnik in programsko opremo za elektronsko in telekomunikacijsko metodologijo za olimpijske igre leta 1992 v Barceloni. Dohodek tega podjetja v letu 1988 je znašal s46m, kar je 20% več kot leto poprej. Tudi podjetja na spodnjem koncu tržišča iščejo priložnosti za svojo razširitev. Npr. podjetje Telmatica e Informatica Internacional je razvilo izboljšano storitev za videotex, ki je dosegljiva prek centrov v več evropskih državah. Drugo majhno podjetje Biochip je izkoristilo množična potovanja po Španiji s prodajo aparaturne in programske opreme za hotelske rezervacijske sisteme. Tudi vlada podpira špansko računalniško industrijo, ko vzpodbuja sodelovanje s tujimi podjetji, toda vpliva na tiste multinacionalke, ki smatrajo, da je Španija le dežela sestav-Ijavcev in izpuh za prodajo; pri tem zagovarja zlasti dejavnosti s področja raziskav in razvoja. Siemens, Olivetti in Unisys imajo v Španiji svoja raziskovalno-razvojna središča. IIP, Olivetti in Buli so se vselili v Valeški tehnološki park v Barceloni, ki je le eden od štirih tehnoloških parkov, v katere je vlada investirala $55m. Fujitsu-Espana ima tri raziskovalno-razvojne centre v Madridu, Malagi in Barceloni, kjer je bila tudi razvita vmesniška plošča za PCjevsko delovno postajo, ki se izvaža v Korejo. Ta gibanja spremlja ministrstvo za industrijo, ki ugotavlja, da se je v Španiji prvič zgodilo to, da pri njih razvijajo nove produkte tudi multinacionalke. To pa je morda veliko pomembnejše od vrste tujih tovarn za sestavljanje. Za vse majhne države so domače raziskave in razvoj zelo drago podjetje. Pri vzpodbujanju sodelovanja s tujci participira Španija tudi v novi program Esprit. Od 155 predloženih španskih projektov jih je bilo sprejetih 74. Ti projekti se tičejo 50 španskih podjetij in 10 univerz. Investronica dela na projektu za razvoj produkcijskega sistema za tekstilno industrijo in podjetje Ibermatica prispeva $750k k $21m, kolikor je predvidenih za projekt, s katerim se razvija generični vizijski sistem za industrijsko uporabo. CCS sodeluje v projektu za vzdrževanje programske opreme in nacionalno telekomunikacijsko podjetje Telfonica v 10 komunikacijskih projektih. V projektih Esprit sodelujejo španske podružnice multinacionalk, npr. Siemens in Katalonska univerza, ki izdelujeta prevajalnik za podatkovne baze; Alcatel Standard Electrica razvija sistem za računalniško podporo za primere katasrofe. Španska vlada je začela uresničevati tudi dru^o fazo svojega Nacionalnega elektronskega in računalniškega projekta (PEIN II), ki se začel v letu 1984. Strategija vlade je, da oblikuje večje industrijske grupacije, še posebej • dve združevalni krovni podjetji (holdinga) za področje telekomunikacij in programske opreme, s ciljem da bi okrepila špansko konkurenčnost do letk 1992. Vladna ministrstva se pooblaščena, da sodelujejo v investicijah v velike projekte informacijske tehnologije, ki naj bi povezovali domorodna in multinacionalna podjetja. Iris je npr. ime projekta v vrednosti $21m, v okviru katerega se razvijajo teleinformacijske storitve in homogena komunikacijska mreža za španski sektor raziskav in razvoja. SCTM je vojaški komunikacijski projekt, Bubi pa je projekt za avtomatizacijo velikih tobačnega naročniškega sistema z vrednostjo $30m. PEIN II je investiral sl50m v elektronske in računalniške projekte že v letu 1984 in s4'80m v letu 1986. Zneska »136m in $144m sta predvidena za investiranje v tem in prihodnjem letu. Španska informacijska industrija pa ne oblikuje le zdrav domači trg, temveč vztrajno povečuje tudi izvoz. Špansko združenje za izvoz elektronike in računalnikov stalno propagira in vzpodbuja izvoz informacijske tehnologije. Investronica je povečala izvoz za 94% v zadnjih petih letih ($30m). Podjetje ne izvaža le v Evropo temveč tudi v Južno Korejo, Japonsko in Argentino. Kljub vsej tej aktivnosti pa je španska informacijska industrija še precej oddaljena od možnosti, da se v letu 1992 pojavi v Evropski skupnosti z vso svojo močjo. Španija mora Se preseči svoj lasten odpor do računalniške uporabe. Videotex je doživel v Španiji popoln neuspeh, saj latinski temperament bolj ceni osebni kontakt. Splošno obotavljanje v uporabi računalnikov je značilnost, katere posledica je npr., da je bilo v letu 1987 v uporabi manj kot 6000 računalniških blagajn in le s 3,4 transakcijami na osebo; v Združenem kraljestvu je znašalo to razmerje 8 transakcij na osebo. Povprečna letna prodaja na kreditne kartice doseže le $85 na osebo. Vse to kaže na določeno informacijsko nespretnost španske populacije in je problem, ki je računalniški industriji znan širom po svetu. KOMENTAR. Španski primer je prav gotovo lahko zanimiv za jugoslovansko in slovensko politiko in podjetništvo na področju informacijske tehnologije. Kaj so naredile vse naše vlade in vladne institucije na področju vzpodbujanja, investiranja in organizacije računalniške industrije? To kar je mogoče z vso zanesljivostjo trditi, je, da niso storile ničesar pomembnega, integrativnega, diplomatskega in nazadnje tudi industrijsko naprednega. Domača računalniška industrija nam je obtičala v spontanem razsulu. Celo napori, da se oblikuje razvojni diskurz med politiko in industrijo, so ostali neuresničeni zaradi pomanjkanja političnega pa tudi podjetniškega interesa. Gospodarska politika se nam je zreducirala na načelo, da naj se vsak rešuje sam. Ali smo posamezniki sploh poklicani in kvalificirani, da se ubadamo s problemi gospodarske in tehnološke politike? Zakaj potem sploh imamo vladne in družbene institucije, ki bdijo nad možnostmi in nujnostmi razvoja? Ko se sprašujem, kako bi lahko vzpodbudno napisal poročilo z naslovom "Informacijska tehnologija v Sloveniji in Jugoslaviji", ki bi bilo primerljivo s Španijo, moram vendarle povedati nekaj več resnice. Španski čudež je seveda ekonomski in šele v okviru tega je mogoče pričakovati spodbudne rezultate v razvoju informatike kljub španskemu•temperamentu in zavračanju informatike kot sodobnega pojava človeštva. Na nek način je celo uspešen španski razvoj vsaj na področju informatike konzervativen, pogojen z mentaliteto populacije. Pri nas je verjetno ta mentalna ovira spektralno SirSa in se ne omejuje le na informatiko, prežema gospodarstvo, podjetništvo in politiko. In dokler je tako, bo informacijski zaostanek le posledica ekonomskega in političnega. In tu bržkone lahko presahne tudi smiselnost vsakrS-nje zasebne pobude. A. P. Železnikar DECove evropske delovne postne prihajajo iz podjetja Olivetti Digital Equipment (DEC) in Olivetti sta se sporazumela, da bo Olivetti dobavljal DECove osebne računalnike za evropsko tržiSče. Osebni računalniki bodo proizvajani po DECovih specifikacijah v Olivettijevih tovarnah in trženi in vzdrževani prek DECovih poslovnih in servisnih organizacij. V okvir tega programa spadajo osebni računalniki s procesorji 80286, 80386SX in 80366, ki oblikujejo podlago za DECove nove osebne delovne postaje. DEC se je odločil za italjanskega proizvajalca, ker je Olivetti močno prisoten na evropskem trgu. A. P. Železnikar Vrednost DECovih akcy je padla Vrednost DECovih akcij je padla za dobrih 10%, ko je postalo znano, da bo dobiček v tretjem poslovnem kvartalu (v marcu 1989) manjši od pričakovanega. Od priSakovanoga porasta dobička 13% do 31. marca je bil dosežen prirastek le 10%. Kot utemeljitev za ta "neuspeh" se navaja poslabšanje na ameriSkem trgu in problemi z novimi produkti. A. P. Železnikar Ali se bodo načrtovalci hardvvara morali naučiti programiranja? mov 2 e do 40 uporabniki. DEC uvaja tudi skupinski (clustered) sistem Microvax in ponuja skupinski Vax. Dva Microvaxa 3800, povezana z DSSI (Digital Storage System Interconnect), bosta dopuSčala katerikoli uporabniški dostop do kateregakoli pomnilnega elementa, ki bo privezan na enega od gostiteljev. Očitno uporablja DEC podobno taktiko, kot"jo je uporabil pri zamenjevanju sistemov 6200 s sistemi 6300, ko ponuja dopolnilne pakete pri samo 5% povečanju cene. A. P. Železnikar Prihaja bržkone čas, ko se bodo ožičevalni inženirji morali sprijazniti s kodiranjem (programiranjem) . Verjetno ste že slišali izrek: hardware je software. (Tudi sam pravim, da je arhitektura ali struktura stroja ali hardware informacija.) Ta čas prihaja, saj načrtovanje hardwara postaja vaja iz kodiranja. Inženirsko delo je v primeru integriranih vezij le §e pisanje koda, ki je čedalje bolj podoben programu v jeziku C ali Adi. Ko je naraSčala popularnost računalniško podprtega načrtovanja, ni bilo težko predvidevati, da bo z računalniki mogoče kmalu sestavljati tabele in ne več risati diagrame (načrte povezanih enot), da bo mogoče definirati module, načrtovalne procedure itd. s programskimi vrsticami. Za te namene je tako nastal jezikovni standard VHDL. Ta okrajšava pomeni: "V" kot VHSIC za pentagonski program Very High Speed Integrated Circuits; HDL pomeni Hardware Description Language. V zadnjem letu je bila v okviru IEEE izdelana verzija jezika, ki ga podpira obrambno ministrstvo ZDA, v igro pa se je vključilo tudi podjetje Mentor Graphics Corp., San Jose, Kalifornija. Prihaja čas, ko se bodo hardwarski inženirji morali začeti učiti pisanja koda v jeziku VHDL. Trg t.i. VHDL-simulatorja je še majhen. Mnogi opazovalci dvomijo, da bodo hardwarski inženirji zmogli radikalni obrat v svojem načinu razmišljanja. Zaradi tega je npr. podjetje Vantage Analysis Systems Inc. skrilo sam jezik pred uporabnikom in s simulacijo prikazalo znane shematične grafe s knjižnjico funkcijskih modelov v VHDL. Ta način načrtovanja pa je brezno, ki ga veliko inženirjev ne bo zmoglo preskočiti. A. P. Železnikar Sistemska integracga DEC napada pisarniško tržišče Digital Equipment je vrgel na tržišče dva računalnika tipa Microvax, s katerima naj bi resno napadel tržišče pisarniške opreme, na katerem gospodujeta sedaj podjetji IBM in Wang. Microvax 3800 in 3900 naj bi zamenjala modela 3500 in 3600 s 50% izboljšanim razmerjem cena/zmogljivost in s štirikratno povečanim obsegom pomnilnika. DEC tudi počasi upokojuje stari in še vedno prodajani Microvax II, ki ga je vrgel na tržišče v letu 1985, ko je znižal ceno aparaturne in programske opreme glede na prejšnje svoje modele. DEC izjavlja, da bo v prvem naletu naskočil tržišče večuporabniških siste- Denar se skriva v t. i. orkestraciji. Padajoči profiti prepričujejo tudi največje računalniške proizvajalce o nujnosti integracije. IBM izjavlja, da bo prodajal Vaxe, če bo dobil dovolj veliko naročilo. En sam računalniški proizvajalec dejansko ne more biti neodvisni sistemski integrator. Letna poročila podjetij so poučna. In v zadnjem času postajajo zgodbe o proizvajalcih aparaturne opreme čedalje bolj žalostne. Trg miniračunalniških izdelkov se bo v letu 1989 bržkone skrčil. Podjetje Control Data je v letu 1988 pridelalo le skromnih sl,7m dobička, norveški Norsk Data pa že izgubo sl29m. Tudi podatki o poslovanju IBM iz zadnjega obdobja kažejo, da se pridobiva dohodek na področjih, ki niso hardwarska. V letu 1987 je plasma softwara prinesel 13% od celotnega prihodka, medtem ko je znašal v letu 1983 le borih 6%. Sporočilo je glasno in jasno: za posel je potrebno imeti kaj več kot le železnino. Zaradi tega ni presenetljivo, da se računalniški proizvajalci pomikajo na področje sistemske integracije. Nič več se ne zadovoljujejo z instalacijo novih mainfrEunov (glavnih računalnikov) s prepuščanjem ostalih postavk v projektu konkurenci ali specialistom s področja računalniških mrež. vse bolj se zavzemajo za vlogo glavnega kontraktorja (pogodbenika) in za kontrolo nad profitom, ki je s tem povezan. V zvezi s tem izjavlja npr. IBM, da bo prodajal DECove Vaxe, če mu bo to pomagalo, da si pridobi posel naročnika. S tem pa se bistveno spreminjajo nekdanje opredelitve velikanov, ki bi v ne tako davnih časih veljale za nesprejemljivo poslovno in tehnološko krivoverstvo. Podjetje Computing Services Association (CSA) navaja, da je bilo v letu 1987 trSiSče softwara in storitev v zapadni Evropi vredno $32bn in četrtino tega dohodka so poželi proizvajalci hardwara. V tej areni se pojavljajo tradicionalni računalniški proizvajalci vključno z IBM, DEC, Unisys in Hewlett-Packard in z njimi se bo ta delež Se povečeval. Toda kateri tržni segment imajo vsi ti proizvajalci v mislih? Ideja o sistemski integraciji je po mnenju CSA predvsem "modna zamisel". Seveda so dobavitelji že od nekdaj poskušali povezovati svoje produkte z napravami drugih proizvajalcev z uporabo mrež in raznovrstnimi drugimi storitvami, če se je to pokazalo kot potrebno. Razlika pa je zdaj v tem, da je bila ta praksa enkapsulirana v termin "sistemska integracija" . Seveda pa se naraščanje sistemske integracije kaže kot dramatično, če se upošteva, da se je zgodila evolucija v smeri koncepta podjetniške in tehnološke koeksistence. Nekateri sicer zatrjujejo, da je termin sistemska integracija znan že 25 let, vendar gre v zadnjem primeru tudi za bistvene terminološke spremembe. Definicija je lahko tudi tale: sposobnost integracije različnih aparaturnih in programskih okolij v enotno poslovno rešitev. To pa je mogoče razumeti in imenovati kot posebno storitev. In treba je priznati, da takšno storitev lahko nudi le dovolj usposobljen in poslovno prožen proizvajalec. Nova paradigma sistemske integracije se je razvila pri uporabnikih. Uporabnik si enostavno želi več storitev. Računalniški centri ostajajo neizkoriščeni zaradi stalnega manka sposobnih kadrov in uporabniki iščejo pomoč tako pri izbiri sistema kot pri njegovi uporabi pri poslovanju. Sistemski integrator mora zato bolj razumeti potrebe uporabnikovih poslov kot pa kaj drugega. To pa je lahko prednost le ustrezno izkušenih integratorjev, ki se ji navadni prodajalci seveda ne morejo približati. Proizvajalci lahko take integratorje najamejo in jih posebej plačajo, medtem pa intenzivno izobražujejo svoje prodajalce. Nič čudnega torej ni, če je kontrolni položaj v obsežnem in zahtevnem projektu visoko cenjen. Zato se večina računalniških podjetij profesionalizira za vlogo t. i. glavnega kon-traktorja v poslih sistemske integracije. Toda tudi večina bi požrla slavo, če bi le lahko bila udeležena pri delitvi dobička. IBM npr. izjavlja, da bi lahko prodal karkoli od zahtevanega, če bi bili posamezni deli sistema dopolnjeni z DECovimi Vaxi ali z Amdahlovim main-framora. Pri tem praktično ni omejitve v tem, kdo vse bi lahko bil subkontraktor. Edina omejitev je poslovno tveganje. Teoretično je sprejemljivo, da se npr. nekaj kupi od DECa in potem preproda. Toda bolj realističen scenarij bi bil povezava novega IBMovega sistema v obstoječo DECovo bazo. Obratno pa bi bilo mogoče tudi k IBMovi bazi dodajati DECove naprave. Zaradi določenih pojavov omahljivosti pri računalniških proizvajalcih, ko gre za sistemsko integracijo, se odpirajo možnosti prav t.i. tretjim integratorjem. Tako se lahko posebna integratorska podjetja ustanavljajo in vzdržujejo za različna področja uporabe s pomočjo računalniških proizvajalcev. Potrebni pa so tudi neodvisni konzultanti, ki jih plačujejo uporabniki. Jasno je pri vsem tem, da se bo področje sistemske integracije moralo še razvijati, preden bo doseglo svoje logične meje, npr. pri gradnji avtomatizirane trgovine in spremljajoče tehnologije v njej. Medtem pa ostaja ključen problem medsebojna povezava podsistemov. Napori podjetja Unisys v smeri odprtih sistemov bi lahko to nalogo olajšali: teoretično bi lahko njegova t.i. Povezava odprtega sistema komunicirala s katerimikoli vstavljenimi stroji. Vendar standarizacija ne bo nikoli dosegla tiste ravnine, na kateri bi hardware postal nepomemben. Tudi če bi Unix postal zares prenosljiv, bodo proizvajalci še vedno lahko inovirali svoje stroje. Glavno načelo sistemske integracije pa ostaja prej ko slej tole: ključna lastnost integracije je, da sistemi delujejo skladno in dovolj učinkovito. To pa naj bi popolnoma osrečilo tudi uporabnike. A. P. Železnikar Računalništvo kot postavje matematike Matematiki so pomagali pri oblikovanju računalniške znanosti, ta pa sedaj povzroča revolucijo svojega lastnega subjekta. Kakšen je ta dramatičen doprinos? Vrsta matematikov se je vpisala v zgodovino računalništva. Charles Babbage je konstruiral predhodnika sodobnega digitalnega računalnika 2e v letu 1830. Alan Turing je definiral svoj abstraktni stroj že v letu 1930 in vplival na razvoj teorije izračunijivosti. John von Neuman je razvil zamisel sekvenčne arhitekture. Medtem je razvoj računalništva že turbulentno vplival na samo matematiko. S prebijanjem skozi suhoparna števila enačb, preiskovanjem milijonov možnosti in z uporabo grafike je ta razvoj povzročil nove koncepte in približal računalnike matematikom kotT njihovo bistveno orodje. Kljub temu pa vrsta matematikov verjame, da računalništvo kompromitira in uničuje fundamentalne vrednote prave matematike. Npr. v letu 1976 sta Keneth Appel in Wolfgang Haken dokazala _ notorični teorem šfiirlh barv. Ta teorem pravi, da je s štirimi barvami mogoče obarvati karterikoli zemljevid tako, da dve sosednji območji nista enake barve. Od leta 1852 dalje so znani matematiki zaman poskušali dokazati ta izrek. Zato je izjava o pravilnem dokazu tega izreka povzročila veliko vznemirjenje. Za vrsto matematikov je bila ta zmaga jalova: dokaz je zahteval uporabo računalnika. IBMov računalnik 360 je odigral ključno vlogo z izračunavanjem tisočev primerov in je pustil matematike v dvomu, kaj bi v bistvu lahko konstituiralo dejanski dokaz. Nobeno človeško bitje ne more verificirati izračunov, toda večina matematikov sprejema te izračune kot veljavne, čeprav je potrebno zaupanje, da računalnik ni naredil napake. Kljub tem težavam, ki se tičejo fundamentov matematičnega subjekta, so ostali matematiki 20. stoletja izredno ustvarjalni. V svoji knjigi "The creative computer" pravita Donald Michie in Rory Johnson: "Že dolgo se napačno predpostavlja, da je iz računalnika mogoče dobiti le tisto, kar jè bilo vanj vstavljeno. ... Sedaj pa je bilo neizpodbitno pokazano, da lahko pride iz računalnika tudi nekaj novega in to novo je znanje. To znanje pa so lahko tudi izvirne ideje, strategije in rešitve realnih problemov." Na prvi pogled izgleda absurdno, da je to res prav v matematiki. Ali je matematika zgolj neka vrsta računalništva oziroma računalniške rutine? Računalništvo kreira novo obliko eksperimentalne matematike, generira, nove matematične strukture in probleme in omogoča nove poti modeliranja zapletenih sistemov z uporabo podatkovnih baz in izračunov. Fraktalna geometrija je le eno od dobro znanih vej nove matematike, ki je omogočena z računalništvom. Njeni antecendenti vključujejo snežinke, ki jih je opisal švedski matematik Helge von Koch leta 1904. Te snežinke je mogoče oblikovati iz enostavnega trikotnika s ponavljanjem "samo-podobnih" operacij na robovih. Čeprav je mogoče matematično dokazati, da ima meja snežinke neskončno dolžino pa ima snežinka končno površino, ki je enaka očrtanemu krogu izvirnega trikotnika. Benoit Mandelbrot, IBMov raziskovalec in oče fraktala, postavlja fractal v zgodovinsko perspektivo krize matematike, ki se je sprožila že z delom Giuseppa Peana. Leta 1890 je Peano definiral krivuljo, ki je zvezna in poteka skozi vsako točko kvadrata. Peanova krivulja omogoča specifikacijo točke z enim samim Številom, z njeno oddaljenostjo od konca krivulje. Opredelitev dimenzije kot števila spremenljivk, ki so potrebne za specifikacijo točke, je postala nevzdržna. Kriza se je končala v letu 1922, ko je Besicovitch predložil končno obliko tega, kar se danes imenuje Hausdorff-Bes±covi-tcheva ali fraktalna dimenzija. V primeru zvezne krivulje se dimenzija nanaša na frakcijo področja ravnine, ki jo pokriva. Mandelbrot definira fraktalno množico kot tisto, ki ima Hausdorff-Besicovitchevo dimenzijo večjo od njene topoloSke dimenzije. Topološ-ka dimenzija ustreza navadno intuitivni ideji dimenzije kogarkoli. Žica je enodimenzionalna, ploSča dvodimenzionalna, bloki so tridimenzionalni itd. Krivulja Peano-Hilberta ima fractal-no dimenzijo 2 in proti-intuitivno je njena topoloäka dimenzija 2. V letu 1979 je Mandelbrot preizkušal tole enostavno iterativno formulo: vzemi neko kompleksno število, ga kvadri-raj, priStej k njemu konstanto in tako naprej. Ali bo končni rezultat divergiral v neskončnost, konvergiral k fiksnemu številu ali izkazoval neko vmesno stanje? Odgovor je, da ležijo konstante, ki povzročajo konvergentno stanje, v obliki hrošča, ki je znana kot Mandelbrotova množica. Vendar je zgodba še zanimivejša: če se Mandelbrotova množica izračunava in prikazuje na zaslonu, se pojavijo posamezni otoki, ločeni od telesa. Vendar matematični izreki pokažejo, da so otoki povezani s telesom množice in ta pojav imenuje Mandelbrot "vražji polimeri". Značilna lastnost teh množic je samo-podobnost. Če računalnik gleda v to množico s povečavo v posamezne njene dele, js mogoče opaziti, da so podstrukture podobne bolj grobim strukturam. Ena najprivlačnejSih vej matematike je trenutno teorija kaosa. Čeprav je ta teorija v tesnem razmerju s fraktali in Mandelbrotovo množico, je pojem kaosa odkril neodvisno od fraktalov Edward Lorentz v letu 1980. Bil je presenečen, ko je odkril, da že majhne spremembe začetnih vrednosti pri simulaciji vremena povzročajo znantno divergenco po preteku določenega časa. Te vrste pojavnost se imenuja kaotičnost. če se predpostavlja, da so enačbe pravilne, to pomeni, da lahko že zelo majhne napake v opazovanju povzročijo dramatične posledice. Ta pojav je mogoče opisati kot metulj-čni efekt: metulj, ki razpre svoja krila danes v Pekingu, lahko oblikuje viharni sistem drug mesec v New Yorku. Morda zveni paradoksalno, da ima kaos strukturo. Množica točk, v kateri obstaja kaotična trajektorija, se imenuje nepričakovani atraktor: atraktor zaradi tega, ker sistem ne pobegne iz njega in nepričakovani, ker nekatere tra-jektorije niso periodične in zaradi načina, kako se trajektorije globoko prepletajo ena z drugo. Računalniško omogočena matematika fraktalov lahko najde pomembno področje uporabe v novi vrsti znanosti o modeliranju komplesnih sistemov, ki so bili doslej deterministično utemeljeni. Teorija avtomatov je nadaljnje področje matematičnega interesa, kot je pokazal John Conway v sijajni Igri življenja (Game of Life). Life je mogoče igrati obsesivno na PCju, ko se generacije barvnih konfiguracij razvijajo na zaslonu. V matematiki se je zgodil bistven premik v smeri, da bi postala eksperimentalna znanost. Obstajajo računalniški paketi, ki pomagajo matematikom pri vsakdanjem delu, podobno kot pomagajo procesorji tekstov pisateljem. Potrebe računalniške znanosti so tudi vzpodbudno vplivale na razvoj novih področij matematike. Pisanje korektnih programov naj bi bilo podvrženo enaki matematični strogosti, kot je npr. oblikovanje tehničnih konstrukcij. Zanesljivost programov postaja čedalje bolj pomembna v industriji programske opreme. Novi specifika-cijski jeziki, kot sta Z in VDM, so zelo blizu matematiki in so utemeljeni z matematičnimi teorijami. Narava metrike v programirni tehniki vzbuja pozornost matematikov, kot je npr. zamisel o programski strukturi. Neglede na povedano pa začenja računalništvo vplivati tudi na poučevanje matematike. Interaktivna barvna grafika lahko znatno poživlja tradicionalno dolgočasna in suhoparna Studijska področja, motivira in ilustrira zapletene ideje in tako zmanjšuje frustracije, ki se pojavljajo ob nepravilnih odgovorih pri trivijalnih napakah izračuna. Naslednje stoletje bo preživljala matematika Srečneje s svojimi računalniki: ojačevanje matematične domiselnosti in možganskih zmogljivosti bo postalo naravno in dobrodošlo kot del vsakdanjika - tako kot sta bila včasih tabla in kreda. Literatura: [1] The Mathematical Revolution Inspired by Computing (Conference held at Brighton Polytechnic on April 5-7, 1989); [2] D. Michie and R. Johnson, The Creative Computer, Pelican 1985; [3] I. Stewart, The Problems of Mathematics, Oxford University Press 1987; [4] K. Devlin, Mathematics: the New Golden Age, Penguin Books 1988; [5] B. Mandelbrot, The Fractal Geometry of Nature, Freeman 1983; [6] Peitgen and Saupe, The Science of Fractal Images, Springer 1988; [7] J. Gleik, Chaos, Heinemann 1987; [8] A. Holden, Chaos, Manchester University Press 1986; [9] W. Poundston, The Recursive Universe, Oxford University Press 1987. A. P. Železnikar IBM je predstavil svoj prvi sistem s procesorjem 80486 IBM prevzema spet vodilno vlogo na področju PC tehnologije. Pred kratkim je predstavil novo tiskano ploščo, ki vsebuje Intelov procesor 80485. S tem je IBM prvi proizvajalec, ki ponuja produkt s procesorjem 80486. Tako v ZDA kot v Evropi se IBM spopada s podjetjem Compaq pri prodaji sistemov s procesorjem 80386. Compaq si je že priboril naskok kot tehnološki prvak na trgu s prvim sistemom 386, s taktno frekvenco 33 MHz, kar omogoča zmogljivost 10 MIPS. S svojo vtično ploščo tipa 486 dovoljuje IBM njeno uporabo v PS/2 modelu 70, kjer doaeie zmogljivost 15 MIPS. Ta zmogljivost pa je bila doslej prihranjena za superminije in spodnje modele mainframov. Nova plošča se nasadi na glavno ploSčo modela 70 in zamenja tako pomnil-niSki vmesni krmilnik B0385, procesor 80386 in koprocesoc. 80387 s procesorjem 80486. V tej zvezi se širijo govorice, da se IBM sploh ne misli pojaviti na trgu s sistemi, ki uporabljajo pirocesor 80386 s taktno frekvenco 33 MHz. A. P. Železnikar Problemi z OS/400 se nada^ujejo Napake v IBMovem računalniku srednje velikosti AS/400 spravljajo v obup uporabnike, saj se s t.i. IBMovim "cepljenjem" pojavljajo še dodatni problemi. S paketom Program Temporary Fix (PTF) nudi IBM uporabnikom možnost, da popravijo napake operacijskega sistema AS/400. Vendar je instalacija PTFa dolgotrajna, napake pa so tudi na traku, ki nosi ta paket; tako so učinki äe poraznejgi kot prej. Pri regularnem odpravljanju napak je potrebno sistem tudi za 24 ur ustaviti in proces s PTF mora biti nadzorovan z živim operaterjem. Pribiližno vsakih Sest tednov izda IBM tudi nov PTF trak. Očitno PTFi Se niso zadovoljivo dozoreli produkti. Število potrebnih instalacijskih korakov naj bi se zmanjšalo iz začetnih 28 na dva koraka. V nekaterih primerih je npr. PTF tudi poruSil celotne dele operacijskega sistema. Problematična je zlasti verzija PTF 1.2. A. P. Železnikar Japonska čaka svojo priložnost na trgu programske opreme Zapadni tržni opazovalci opozarjajo na ofenzivo, ki prihaja z Daljnega vzhoda. Japonska softwarska industrija se pripravlja za napad na zapadna tržiSča. V svetovnem merilu je položaj ZDA na področju programske opreme drugim zaenkrat nedosegljiv. Ameriška podjetja izdobavijo 70% vseh softwarskih produktov na svetu in so s 50% najpomembnejša uporabniška država. Svetovno tržišče, ki je bilo za leto 1988 ocenjeno na »50bn, naj bi po mnenju ekspertov do leta 2000 eksplodiralo na več kot 1000 milijard dolarjev (slOOObn). Japonci so doslej že ugotovili svoje slabosti na področju programske opreme in ob primerni organizaciji in razpoložljivem kapitalu bi se položaj lahko hitro spremenil.. Fujitsu je že leta 1983 ustanovil svoje podjetje v Silicijski dolini, kasneje pa Se Sony v Palo Alto, Hitachi v San Bruno in Ricoh v Santa Clari. Japonska aktivnost se običajno dolgo časa skriva in je ni mogoče ocenjevati. Podjetja na Daljnem vzhodu nenehno povečujejo napore za obvladovanje proizvodnje programske opreme. Hitachi usmerja že 30% raziskovalnih in razvojnih aplikacij v software. Toshiba je pred kratkim odprla tovarno softwara s 3000 programirnimi specialisti za razvoj komercialnih in industrijskih programov. Tudi NEC namenja s400m letno v razvoj programske opreme. Ameriški eksperti predvidevajo, da bodo Japonci in drugi Azijci stopili na trg softwara s strategijo treh poti: najprej prek hardwara za odpiranje trga, potem prek sistemskega softwara tja do uporabniške programske opreme. Pri tem jim lahko pomaga tudi Unix. Samo Sanyo ima že 100 tehniških in grafičnih paketov za svoje delovne postaje, ki jih ponuja v okolju Unixa. Pri vsem tem pa bo treba premagati Se marsikatero oviro. Ovire pa niso le vpraSanja jezika in razlike v mentaliteti, temveč tudi'izobraževalni problemi. Izračunali so, da bi Daljni vzhod potreboval leta 1990 že 1,6 milijona sodelavcev, na razpolago pa jih bo le pičel milijon. A. P. Železnikar Deja vu videotexa Beli dokument Evropske skupnosti vsebuje med drugim tudi načrt, kako naj bi se računalništvo in informatika na velikem skupnem trgu uveljavljala z uporabo videotexa pri vsakdanjem nakupovanju. Do nedavnega je ameriSJti potrošnik odklanjal videotex, ki je bil v ZDA 2e v letu 1980 uveden kot informacijska storitev. Videotex je npr. propadel. tudi v Španiji. V zadnjem času pa poskuSata trgovsko podjetje Sears in IBM spremeniti to odklonilno držo Američanov z novimi podatkovnimi in vizualnimi možnostmi pri nakupovanju. Sears je največja ameriška trgovska hiša za prodajo na drobno. IBM je največje računalniško podjetje na svetu. In ti dve podjetji sta zdaj povezali svoje marketinške in tehnološke mišice s ciljem, da zgradita nov sistem elektronske pošte za informiranje in nakupovanje. Ime tega projekta je Prodigy (slovensko: čudo). Prodigy združuje besedilo in grafiko v obliki živega prikaza in prinaša novice, vremensko stanje in napoved, nakupovanje, razvedrilo, izobraževanje, potovanje, finančne storitve in časopisne izvlečke na dom ali v službo prek PCja. Trenutno je Prodigy na razpolago le na regionalnih trgih, že drugo leto pa bo dostopen na celotnem ozemlju ZDA. Seveda je zanimiva tudi cena. Za programsko opremo, identifikator in prosti dostop za prve tri mesece bo potrebno odšteti s49,95. Enak paket, toda z modulom za 1200 baudov, ki se ga vstavi v PC, ima ceno »149,95. V tej ceni je zajetih Sest družinskih članov, od katerih ima vsak svoj identifikator. Konfiguracija PCja pa je tale: IBMovsko združljivi PC mora imeti vsaj 512k RAMa, grafični adapter, diskovni pogon in že omenjeni modem za 1200 baud. Seveda pa bo mogoče uporabljati tudi Applove in Macintoshove računalnike. Ali bo Prodigy uspel tam, kjer so drugi 2e propadli? A. P. Železnikar Virusna hister^a Kako se je mogoče izogniti virusni histeriji, ki je zajela tako uporabnike PCjev kot mainfra-mov? Virusni programi se pojavljajo v različnih izvedbah in tudi na različnih koncih sveta, od ZDA do Sovjetske zveze. Pred to nadležno in predvsem škodljivo infekcijo se je mogoče obvarovati s posebno zaščitno strategijo, s posebno kontrolo sistemskih in uporabniških programov preden jih spustimo v obratovanje na naših računalnikih. Jet Propulsion Laboratory (JPL) v Passadeni (Kalifornija) se je v preteklem letu okužil s Stirimi vrstami virusov, ki so napadle tako trdne diske kot tudi povzročile prekinitve ' dela. Pri virusni zaSčiti priporoča JPL dovolj pogosto shranjevanje (backup) in testiranje-naložene programske opreme s programi za detekcijo virusov pred njihovo uporabo. V tem primeru so lahko softwarski virusi manj učinkoviti v svoji razdiralni funkciji. V decembru 1988 se je v iBMovi korporativni mreži pojavil virus, ki se je javljal na zaslonih 2 božičnimi čestitkami. Programski virusi se pri nekaterih uporabnikih razumevajo podobno kot terorizem in AIDS. Ker so računalniki povezani v mreže, nastaja občutek, da lahko slučajen kontakt ob nepravem času povzroči katastrofo. Najbolj znani primer, ki je bil podoben katastrofi, se je primeril v vladni mreži v novembru 1988, povzročil pa ga je študent R. Morris s Cornellske univerze. Ta virus sicer ni uničeval podatkov, se je pa tako hitro razmnoževal, da so bile mreže prek celotnega kontinenta že v nekaj urah preobremenjene. Če bi bil ta virus konstruiran še za rušenje podatkov, bi lahko povzročil maščevalno opustošenje v računalniških sistemih širom po deželi. Zanimivo pa je, da Morris ni bil obtožen za kriminalno dejanje in obstaja dvom o obstoju možnosti, da bi ga po obstoječi ameriški zakonodaji sploh bilo mogoče obtožiti. Del teh težav izvira iz dejstva, da vsebujejo tudi legalni programski paketi "viruse". To so lahko nenamerni (tudi neidentificirani) virusi, ki se seveda razlikujejo od zlonamernih. T. i. 13. virus programa Friday (ki je uničil podatke na osebnih računalnikih v Izraelu, Londonu in v JPL) lahko postane bolj splošen. Nekateri so prepričani, da je ta virus le del ledene gore. Prihaja doba t.i. usmerjenih virusov in ta virusni pojav je praktično neomejen. Usmerjeni virusi se oblikujejo s posebnimi nameni in se sčasoma tudi spreminjajo. Specialisti za virusno zaščito poročajo o virusih, ki lahko porušijo korporativno mrežo v določenem časovnem intervalu in povzročijo izgubo zaradi padca produktivnosti korporacije. Pred ameriškimi sodišči pa se že pojavljajo primeri, s katerimi se izterjuje odškodnina, ki jo je kdo utrpel zaradi namernega virusa. To seveda pomeni, da programska oprema vobče ne bi smela biti zaščitena z virusnimi programi, ali pa vsaj ne s takimi, ki lahko poškodujejo druge programe in podatke. Piratska programska oprema je drugi nepredvidljivi izvor virusov, ki ga 'praktično ni mogoče kontrolirati. Eden od najbolj razširjenih virusov je nastal v računalniški trgovini v Lahore (Pakistan), kjer sta dva brata, Paki-stanca vgradila virus v piratske kopije Lotusa 1-2-3, Wordstara in v druge popularne aplikacije, z namenom, da kaznujeta tiste, ki kupujejo piratski software. V tej trgovini so kupovali programsko opremo turisti in poslovneži, ki so obiskali Lahore. Nekateri virusi so lahko tudi takšni, da se oprimejo konkurenčnega softwara, ko so bili vnešeni v sistem in s tem okrnijo ugled proizvajalca izvirne programske opreme. Eden prvih komercialnih paketov z virusom je bil Freehand podjetja Aldus Corp. za Macinto-sha. Ta virus sporoči prek zaslona vsem Macin-toshovim uporabnikom mir na svetu, potem pa izgine. Drugi virus napade CD-ROM in uniči podatke. Freehandov virus je dobil ime mirovni virus in je šolski primer, kako se lahko virus hitro razširja. Ta virus je konstruiral D. Davidson v Tucsonu (Arizona) in ga poslal R. Brandowu, ki ga je spravil na diskete z igrami v Macintoshovi skupini uporabnikov. Kmalu je bilo s tem virusom okuženih na tisoče disket. Seveda je vprašanje, kakšni so virusni simptomi. .Biološki virus povzroča npr. nahod in vročino. Pri računalniškem virusu se zgodi nekaj podobnega. Ti simptomi so lahko upočasnjeno delovanje računalnika, saj veliko število virusov znižuje zmogljivost, ko se dovolj razmnožijo. Drugi opozorilni znaki pa so: dostopa-nje na disk brez zahteve in nepredviđeno zmanjšanje razpoložljivega pomnilnika. Uporabniki sistemov z DOS naj bi kot prvo zaščitno operacijo izvajali program CHKDSK. Ta storitev pove, koliko prostora na trdnem disku je v uporabi, koliko je skritih zbirk in koliko Je zgubljenih skupin (clusters). Če se kateri od teh podatkov naenkrat spremeni, je velika verjetnost, da Je na delu virus. Programi za detekcijo virusov, ki so na trgu, so primerni za opazovanje virusov. Ti paketi zagotavljajo, da bodo z njimi virusi odkriti in tudi odstranjeni. Seveda pa to velja le za najbolj znane oziroma razSlrJene viruse. Oglejmo si nekaj komercialnih paketov za detekcijo in odstranjevanje virusov. MultiPlus je v ROMu rezidentna storitev podjetja SunPlox Software (Atlanta), ki je sploSna programska oprema za opravljanje virusne detekcije. Mace 5 podjetja Mace Utilities vsebuje kodno zaščito proti virusom. Paket Murray podjetja Emst & whinney nudi širšo zaščito, kot je zaščita z geslom in zaklepanje zbirk vključno z virusno detekcijo. Dobijo se tudi zaščitni paketi, ki se prodajajo skupaj z vsakim trdnim diskom (Arche Technologies). Program naredi virusni preizkus ob vsaki vključitvi računalnika in odstrani najdene viruse. Immune System pa Je že računalnik s procesorjem 80286, ki Je virusno varen. Ima specialno zaščiteno jedro operacijskega sistema, ki onemogoča spremembe v DOS in BIOS, uporablja geslo in program za zbirčno omejevanje (American Computer Security Industries). Podobna naprava za obstoječe računalnike je plošča Immunetec PC (Zeus Corp.), ki preizkuša sistemske zbirke DOSa in nalagalnl sektor trdnega diska na kakrSenkoli virus. Immunetec PC omogoča sistemsko administracijo z namenom, da preprečuje nalaganje z disket in da postavlja gesla in avtorizacijske ravnine. Drugi ploščni produkt Je Trispan (Micronyx), XI zagotavlja virusno zaščito posameznim uporabnikom v mreži. Trispan preizkuša sistemske zbirke na spremembe zaradi virusa in nudi zaščito, kot je krmiljeni mrežni dostop, gesla, šifriranje in revizija uporabniških poti. Priporočila, ki se v povezavi z virusno programsko opremo pojavljajo, so kratko tale: 1. Programsko opremo Iz t.i. javne domene (tudi iz divjega trga) preizkusi s programi za detekcijo virusov pred uporabo na lastnem sistemu . 2. Shrani izvirne aplikacijske diskete tako, da se ne morejo okužiti. 3. Opravljaj pogosto rezervno shranjevčmje (backup). 4. Čimbolj omeji izmenjavo disket, ki vsebujejo izvršljivi kod (npr. zbirke tipa .exe in 5. Postavi pisalno zaščito (write-protect tab) na vse diskete. 6. Nikoli ne nalagaj sistem s trdnim diskom iz diskete, ki ni originalna ali iz diska, ki ni pisalno zaščiten. 7. Virusna varnost (varnost pred virusi) naj bo le razSiritev splošne varnosti; ne obravnavaj je kot posebno varnost. 8. Poučenost in zavest o virusnem problemu sta najboljša pot, da se s tem problemom soočiS. A. P. Železnikar Programska in aparaturna oprema za virusno zaščito na IBMovskih PCjih Certus ($189) je paket za DOS, s katerim se oblikuje mojstrska zbirka vseh zbirk in ta kopija se primerja kasneje z zbirkami ne disku. Program zapisuje spremembe, ki indicirajo viruse in sporoča rezultate. Iz tega je mogoče sklepati, kdaj in kje se je virus pojavil. Certus tudi blokira tiste pisalne dostope, ki naj bi se opravili mimo DOSa. Približno 8k programa je stalno v RAM pomnilniku. Proizvajalec: Foundation. Ware, 13110 Shaker Sq., Cleveland, OH 44120. C-4 (s40) je paket za DOS in je stalno v RAMu. Opazuje zneunenja prisotnosti virusov in takoj zamrzne program, ko zazna virus. Pri tem identificira območje delovanja virusa. Po tej transakciji je mogoče delo nadaljevati ali pa ustaviti sistem in ukrepati v smislu odstranitve virusa. Drugi program podjetja InterPath, ki se iraenuja Tracer ($50), zapisuje sistemsko informacijo, in sicer status zbirk CONFIG.SYS, kah. ObveSča o spremembah, takoj ko jih najde. Proizvajalec: InterPath, 4423 Cheeney St., Santa Clara, CA 95054. Disk Watcher ($100) preizkuša na viruse v okviru DOS na dva načina. Najprej naredi preskus na prisotnost virusa pri vsakem vklopu sistema. Nato preide v poseben pomnilniško rezidenten način (zesede približno 50k RAMa) in kontinuirano opazuje sistem glede na viruse. Disk Watcher razpolaga tudi s storitvenimi funkcijami, ki npr. preprečujejo nepričakovano formatiranje in brisanje zbirk. Proizvajalec: RG Software Systems, Inc., 2300 Computer Ave., Suite 1-51, Willow Grove, PA 19090. MultiPlus ($99) je rezidentna storitev (do lOOk) za IBMovski PC, ki vsebuje program za detekcijo in odstranjevanje virusov. Storitev vključuje besedni procesor, zbirčni upravljal-nik, avtomatični izbiralnik, razmeščevalnik in kalkulator. Virusni del programa identificira programe, ki dostopa jo v .EXE in .COM zbirke ali na trdni disk. Pri zaznavi virusa se sproži sporočilo in navodilo za nadljnjo akcijo. Proizvajalec: SunFlex Software, 1447 Peachtree St., Suite 503, Atlanta, GA 30309. Virus-Pro ($50) je zaščita pred virusi v več stopnjah, in sicer z zapisovanjem statusa DOS zbirk (tipa . EXE in drugih) na originalnih disketah in na trdnem disku. Program primerja stanje originalnih in kasnejših zbirk in če najde razliko, generira sporočilo o spremembah. Proizvajalec: International Security Technolo-' gy, Inc., Suite 1710, 515 Madison Ave., New York, NY 10022. Immunetec PC ($295) je plošča za IBMovski PC ki preizkuSa DOS sistemske zbirke in nalagalni sektor trdnega diska na prisotnost virusov. Ker je kompatibilna z Novell, 3Com in IBM token ring vezji, omogoča ta plošča sistemskemu administratorju, da ta zaščiti sistem pred nalaganjem z diskete. Administrator lahko postavlja tudi gesla in avtorizirane ravnine dostopa. Zeus namerava uvesti verzijo ploSče, ki bi bila kompatibilna tudi z IBMovim PS/2. Proizvajalec: Zeus Corp., 538 Palisades Dr., Akron, OH 44303. Trispan ($895) je IBMovska plošča za preizkušanje sistemskih zbirk, ki se spremenijo zaradi virusov. Obstajajo tudi drugi varnostni preizkusi vključno z možnostjo zaščite z gesli, šifriranjem in oblikovanjem revizijskih sledi na sistemu ali v mreži. Proizvajalec: Micronyx, Inc., 1901 N. Central Expressway, Richardson, TX 75080. A. P. Železnikar Natančnejša virusna detekcga Kakšna je metoda za natančnejše preskuSanje zbirke command.com? Pri tem se lahko uporabi storitev za primerjavo DOS zbirk z imenom fc.exe. Najprej kopirate vašo originalno zbirko. command.com na vaš trdni disk, in sicer pod modificiranim imenom, kot je npr. command.tst. Potem dodate posebno vrstico na koncu vaSe zbirke (z uporabo EDLIN ali drugega beeedega procesorja, ki generira ASCII zbirke), in sicer FC/B COMMAND.COM COMMAND.TST T.i. /B stikalo, ki povzroči binarno primerjavo, sicer ni nujno, ker ima ena od primerjanih zbirk že sufiks .com, tako da bi se binarna primerjava tako ali tako izvršila. Vsakokrat ko pri vklopu naložite vaš sistem, bo ta ukaz primerjal ti dve zbirki zlog za zlogom. Če sta enaki, se bo pojavilo sporoCilo FC: No difference encountered Če pa so razlike, bodo te prikazane. Druga zaščitna mera proti virusom je izvajanje komunikacijskih programov iz t. i. RAM diska. Vse, kar se naloži prek modema, se najprej shrani v RAM disk in od tu se kopira na disketo. Nikoli naj ne bi kopirali naloženo zbirko na trdni disk, dokler niste prepričani, da je zbirka brezhibna. Te, dokaj enostavne zaščitne mere niso absolutne, nudijo pa lahko kar občutno zaščito pred virusi. A. P. železnikar Avtorsko stvarno kazalo časopisa Informatica, letnik 13 (1989) Authors' Subject Index of the Journal Informatica, Volume 13 (1989) ČLANKI Acketa, D.M., Violeta Hank, and D. Surla, On the Intersection of Two Convex Polygons, informatica 13 (1989), No. 4, 52-57. Barle, J. and J. Grad, Assuring Numerical Stability in the Process of Matrix Rafactori-zation within Linear Programming Package on PC. informatica 13 (1989), No. 4, 38-43. Bogunivid, N. , Syntactic Parsing and Plotting of Mathematical Expressions. Informatica 13 (1989), No. 1, 6-10. Colnarič, M. and I. Rozman, Survey of the MAP Project. Informatica 13 (1989), No. 2, 43-48. Ćosić, K., I. Miler, and I. Rageta, Design and Testing of Homogenous Single Bus Tightly Coupled Multiprocessor System for Real Time Simulation. Informatica 13 (1989), No. 3, .1-13. Debevc, M., R. Svečko in D. Đonlagić, Komunikacija človek-računalnik v regulacijski tehniki. Informatica 13 (1989), No. 2, 52-55. Đonlagić, Jasna in N. Guid, Fraktali - znanost ali umetnost. Informatica 13 (1989), No. 4, 5868. Dreo, G., B. Horvat, and R. Slatinek, ISDN User-network Interface Layer 3. Informatica 13 (1989), No. 3, 14-20. Gerkeš, M., Synthesis in Complex Problem Domains, Informatica 13 (1989), No. 4, 1-15. Jereb, B., L. Pipan in A. Klofutar, Transputerji. Informatica 13 (1989), No. 1, 4347. Jereb, B. in L. Pipan, Merjenje paralelnosti algoritmov. Informatica 13 (1989), No. 3, 4649. Jeremić, L., Z. Budimac i Mirjana Ivanivić, Primana metoda inženjerstva znanja u obrazovanju. Informatica 13 ^989), No. 4, 69-71. Kapus, Tatjana and B. Horvat, Formal Verification of Distributed Systems. Informatica 13 (1989), No. 4, 44-47. Kononenko, I., Nevronske mreže. Informatica 13 (1989), No. 2, 56-71. Kribel, Z., B. Legac, M. Marušič in A. Novak, Izbor programskega orodja četrte generacije. Informatica 13 (1989), No. 1, 22-24. Mahnič, V., Implemetacija poizvedovanj v mrežnih datotekah. Informatica 13 (1989), No. 3, 50-60. Miladinović, R. and D. VelaSević, Relational Schema Description Language. Informatica 13 (1989), No. 1, 11-21, Piskar, R./ Reliability Prediction of Parsys Hypercube Architecture. Informatica 13 (1989), No. 2, 49-51. Prešern, S., P. Brajak, L. vogel, and A.P. Železnikar, An Adaptable Parallel Search of Knowledge Bases with Beam Search. Informatica 13 (1989), No. 2, 35-42. PreSern, S., L, Gyergyek, A.P. Železnikar, and Sonja Jeram, Neural Network Based Parallel Expert System. Informatica 13 (1989), No. 3, 61-64. Race, I.Z., Mogućnosti proceduralnog programiranja u programskom jeziku Prolog. Informatica 13 (1989), No. 3, 41-45. Radovan, M., Modeliranje podataka: ER jezik i normalne forme. Informatica 13 (1989), No. 1, 67-78. Rozman, I. and Maja Drev, Why Informatica Cannot Be Covered by the SCI? Informatica 13 (1989), No. 2, 81-82. Rugelj, J., Upravljanje porazdeljenih sistemov. Informatica 13 (1989), No. 1, 53-57. Rugelj, J., Upravljanje z imeni v porazdeljenih sistemih. Informatica 13 (1989), No. 2, 77-80. Rupnik, v.. Ocena informacijske Škode stroškovno in dohodkovno transformiranih proizvodnih sistemov. Informatica 13 (1989), No. 1, 48-52. špigel. I., Integral, Implicitly Intelligent Systems. Informatica 13 (1989), No. 2, 1-5. Tvrdy, Helena, Porazdeljeni elektronski imenik. Informatica 13 (1989), No. 1, 79-87. Vidmar, T. in J. Virant, Rekurzivni postopek testiranja večnivojskega komunikacijskega sistema. Informatica 13 (1989), No. 2, 72-76. Žagar, A. and P. Brajak, Interconnection Network Analysis and Logic Design. Informatica 13 (1989), No. 2, 24-34. Železnikar, A.P., Possibilities of Parallel Information Processing in the 1990's. Informatica 13 (1989), No. 1, 3-5. Železnikar, A.P., Informational Logic III. Informatica 13 (1989), No. 1, 25-42. Železnikar, A.P., Informational Logic IV. Informatica 13 (1989), No. 2, 6-23. Železnikar, A.P., Informacijski principi in formalizacija. Informatica 13 (1989), No. 3, 21-40. Železnikar, A.P., An Informational Theory of Discourse I, Informatica 13 (1989), No. 4, 1637 . Žerovnik, J., Verjetnostni model računanja. Informatica 13 (1989), No. 1, 58-66. Žunić, J. and I. Stojraenović, Characterization of Circuits in Grid Obtained by Regular and Semi-regular Tessellations. Informatica 13 (1989), No. 4, 48-51. Informacijska tehnologija v Španiji (A.P. Železnikar) Informatica 13 (1989), No. 4, 84-85. Intel's ISSCC Bombshell: A Supercomputer on a Chip (P. Hitij) Informatica 13 (1989), No. 3, 70. Japonska čaka svojo priložnost na trgu prograia-ske opreme (A.P. Železnikar) Informatica 1,3 (1989), No. 4, 89. Mednarodna poletna šola "Constructive' Methods in Computing Science", Marktoberdorf, Zvezna republika Nemčija, 24.7.-5.8.1988 (Tatjana Kapus) Informatica 13 (1989), No. 1, 90. FORUM INFORMATIONIS PreSern, S., Poročilo s tretjega zasedanja Forum Informationis. Informatica 13 (1989), No. 3, 65-67. NOVICE I N ZANIMIVOSTI Ali se bodo načrtovalci hardwara morali naučiti programiranja? (A.P. Železnikar) Informatica 13 (1989), No. 4, 86. Analogni nevralni procesor podjetja Fujitsu (A.P. Železnikar) Informatica 13 (1989), No. 3, 74. BrainMaker: simulator nevralnih vezij (A.P. Železnikar) Informatica 13 (1989), No. 3, 74. DEC napada pisarniško tržišče (A.P. Železnikar) Informatica 13 (1989), No. 4, 86. DEC se pomika v komunikacijsko integracijo (A.P. Železnikar) Informatica 13 (1989), No. 3, 75-76. DECove evropske delovne postaje prihajajo iz podjetja Olivetti (A.P. Železnikar) Informatica 13 (1989), No. 4, 85. Deja vu videoteksta (A.P. Železnikar) Informatica 13 (1989), No. 4, 89. Deset principov strategije industrijskega računalniškega pšodjetja (A.P. Železnikar) Informatica 13 (1989), No. 3, 70-71. Ekološke raziskave poklicnega programiranja (A.P. Železnikar) Informatica 13 (1989), No. 3, 72-73. EUREKA sproža skupni programirni projekt (A.P. Železnikar) Informatica 13 (1989), No. 3, 74. Finančne in razvojne novice (A.P.Železnikar) Informatica 13 (1989), No. 3, 73. IBM je predstavil svoj prvi sistem s procesorjem 80486 (A.P. Železnikar) Informatica 13 U989), No. 4, 88-89. \ IBM sprejema mrežni standars OSI (A.P, Železnikar) Informatica 13 (1989), No. 3, 75. Na rob konferenci o zanesljivosti in kvaliteti (R. Piskar) Informatica 13 (19,89), No. 4, 8384. Nastajamja mlade informatike (A.P. Železnikar) Informatica 13 (1989), No. 3, 74-75. . Natančnejša virusna detekcija (A.P. Železnikar) Informatica 13 (1989), No. 4, 91. Nevralna vezja tudi v tovarni (A.P. Železnikar) Informatica 13 (1989), No. 3, 74. Od ptičjega petja, do nevrogeneze (A.P. Železnikar) Informatica 13 (1989), No. 3, 72. O globalni logiki strateških koalicij (A.P. Železnikar) Informatica 13 (1989), No. 3, 7778. Optična rešitev (A.P. Železnikar) Informatica 13 (1989), No. 3, 76. Philips vstopa v proizvodnjo dinamičnih rajnov (A.P. Železnikar) Informatica 13 (1989), No. 3, 76. Problemi z OS/400 se nadaljujejo (A.P. Železnikar) Informatica 13 (1989), No. 4, 89. Programska in aparaturna oprema za virusno zaščito na IBMovskih PCjih (A.P. Železnikar) Informatica 13 (1989), No. 4, 91. Računalništvo kot disciplina (A.P. Železnikar) Informatica 13 (1989), No. 3, 77. Računalništvo kot postavje matematike (A.P. Železnikar) Informatica 13 (1989), No. 4, 87-88. Sistemska integracija (A.P. Železnikar) Informatica 13 (1989), No. 4, 86-87. Transputer - mikroprocesor, ki prihaja (A.P. Železnikar) Informatica 13 (1989), No. 3, 7172. Virusna histerija (A.P. Železnikar) Informatica 13 (1989), No. 4, 89-91. Vojaške raziskave postajajo komercialne (A.P. Železnikar) Informatica 13 (1989), No. 3, 77. Vrednost DECovih akcij je padla (A.P. Železnikar) Informatica 13 (1989), No. 4, 85-86. Z ekspertnim sistemom proti propadanju podjetij (Prenos znanja v računalnike) (A.P. Zeleznikar) Informatica 13 (1989), No. 3, 68-69. Zakaj se inZenirji zavzemamo za tehnoloSko tržno združevanje (R. Piskar) Informatica 13 (1989), No. 4, 82-83. STRATEGIJA RAČUNALNIŠTVA Ali IBM lahko postane največje telefonsko podjetje na svetu (A.P. Železnikar) Informatica 13 (1989), No. 4, 72-73. Digital Equipment v letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 78. Finska Nokia na pohodu (A.P. Železnikar) Informatica 13 (1989), No. 4, 81. Prancoski Croupe Bull v letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 80. Fujitsu v preteklem letu (A.P. Železnikar) Informatica 13 (1989), No. 4, 78-79. IBM v preteklem letu (A.P. Železnikar) Informatica 13 (1989), No. 4, 77-78. Izgubarji in nazadovale! v računalniški industriji v letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 76. Kovanje denarja z delovnimi postajami ali Sun Microsystems v letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 81. Največji prihodek na zaposlenega v računalniSki industriji leta 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 76-77. Poslovni podatki za räSunalniSka podjetja na svetu v koledarskem letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 75-76. Prestrukturiranje podjetja Olivetti glede na novo realnost (A.P. 'Železnikar) Informatica 13 (1989), No. 4, 79-80. Računalniška podjetja z največjo donosnostjo v letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 77. Računalniška podjetja z največjo rastjo prihodka v letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 77. Siemens v letu 1988 (A.P. Železnikar) Informatica 13 (1989), No. 4, 79. Trije trgi oblikujejo računalniško industrijo (A. P. Železnikar) Informatica 13 (1989), No. 4, 73-75. TORKOVI IN PETKOVI POGOVORI Kako so nastali torkovi pogovori. Informatica 13 (1989), No. 3, 82. Petkovi pogovori. Informatica 13 (1989), No. 4, 95. Terčelj, A., Grafični standardi v luči uporabniške povezave. Informatica 13 (1989), No. 3, 82. ■ Železnikar, A. P., Razvojni credo Slovenije in Iskre Delte. Informatica 13 (1989), No. 3, 7982. INFORMACIJSKA KOZERIJA Železnikar, A.P., Na rob zgodbi o ražunalniSkem razumevanju. Informatica 13 (1989), No. 3, 8384. SOME RECENTLY PUBLISHED PAPERS IN FOREIGN PROFESSIONAL PERIODICALS Informatica 13 (1989), No. 2, 82. Informatica 13 (1989), No. 3, 84. Informatica 13 (1989), No. 4, 95. POPRAVKI Popravek naslova avtorja B. Jereba. Informatica 13 (1989), No. 4, 95. - VME-modul s procesorjem 80386 (D. Novak, Mikra) - računalniške mreže v Sloveniji, SFRJ in Evropi (A. Delničar) - komercialne možnosti uporabe nevralnih mrež in proizvodnje nevronskih računalnikov (S. Jeram) - grafični standardi (dopolnitev) (D. Pungerčar) Drugi pogovor (16. junija 1989) je obravnaval tele teme: - informacijska tehnologija v Španiji (A. P. Zeleznikar) - računalniško podprto projektiranje tiskanih vezij na miniračunalnikih (S. Jemec) - dodatna orodja za projektiranje tiskanih vezij (M. Kovačevič, Mikra) Pogovora je moderiral prof. dr. Anton P. Zeleznikar, udeležili pa so se ju uslučbenci delovnih enot razvoja, raziskav, prodaje, vodstva in organizacije in zunanji sodelavci. Popravek naslova avtorja B. Jereba v naslovu članka "Merjenje paralelnosti algoritmov", Informatica 13 (3) 46-49 je bila ob avtorju B. Jerebu objavljena DO Institut J. Stefan. Delo, ki ga obravnava članek, je nastalo _p.r-i -usposabljanju r a z i-s k ova lea -B . Jereba na IJS, dočira je naslov njegove matične DO Gorenje Raziskave in razvoj. Za nastalo nelogičnost se uredništvo opravičuje avtorju in njegovi DO. Da tudi v prihodnje ne bi prihajalo do zagate, ki bi se lahko pojavila ob tako dolgem pojasnilu v samem naslovu, se avtorji naprošajo, da daljša pojasnila postavijo v opombo na prvi strani prispevka. Urednik Attention to the Readers of Informatica Petkovi pogovori Peliovi pogovori so nadaljevanje torkovih pogovorov in so stiBkovni informativni forum Poslovne enote za razvoj, raaffikave in innovacije Iskre Delte, na katerem teče pO(gDvor o najnovejših dosežkih računalništva in isjfarmatike po svetu in v podjetju, in sicer z vidika Irfamologije, uporabe in znanosti. Opravljena sta bila le èva petkova pogovora. Pm pogovor (12. maja 1989) je obsegal naslednje teme: — DECova in IBMova strategija mrež standarda OSI (A. P. Zeleznikar) Readers of Informatica are kindly requested to send information on their papers recently published in foreign professional (scientific, also philosophical) journals (periodicals). Such information will be regularly published within this column. Some Recently Published Papers in Foreign Professional Periodicals Z. Brezočnik and B. Horvat, Automatic Formal Verification of Digital Systems Using Prolog. ACM/SIGCHI 19 (1988), No. 4, 13-14 (ACM Press). Informatica Editor - in - Chief ANTON P. (aELEZNIKAR Iskra Delta Computers Production Center Stegne 15C 61000 Ljubljana PHONE: ( + 38 61) 57 45 54 TELEX: 31366 yu delta FAX: ( + 38 61)'32 88 87 and. ( + 38 61) 55 32 61 ELECTRONIC MAIL: ...uunet!mcvax!idc\Tiug!idcIike Associate Editor RUDOLF MURN Jo'ef Stefan Institute Jamova c. 39 61000 Ljubljana Editorial Board Publishing Council SUAD ALAGIC Faculty of Electrical Engineering University of Sarajevo Lukavica - Toplička bb - 71000 Sarajevo DAMJAN BOJADŽIEV Jožef Stefan Institute Jamova c. 39 61000 Ljubljana JOZO DUJMOVIČ Faculty of Electrical Engineering University of Belgrade Bulevar revolucije 73 11000 Beograd JANEZ GRAD Faculty of Economics E. K. University of Ljubljana Kardeljeva ploSčad 17 61000 Ljubljana BOGOMIR HORVAT Faculty of Engineering University of Maribor Smetanova ul. 17 62000 Maribor UUBO PIPAN Faculty of Electrical Engineering and Computing E. K. University of Ljubljana Tržaška c. 25 61000 Ljubljana TOMAŽ PISANSKI Department of Mathematics and Mechanics E. K. University of Ljubljana Jadranska c. 19 61000 Ljubljana OLIVER POPOV Faculty of Natural Sciences and Mathematics C. M. University of Skopje Gazibaba bb 91000 Skopje SASO PRESERN Iskra Delta Computers Production Center Stegne 15C 61000 Ljubljana VIUEM RUPNIK Faculty of Economics E. K. University of Ljubljana Kardeljeva ploščad 17 61000 Ljubljana BRANKO SOUČEK Faculty of Natural Sciences and Mathematics University of Zagreb Marulicev trg 19 41000 Zagreb TOMAŽ BANOVEC Zavod SR Slovenije za statistiko Vožarski pot 12 61000 Ljubljana ANDREJ JERMAN- BLAŽIČ Iskra Telematika Trg revolucije 3 61000 Ljubljana BOJAN KLEMENČIČ Turk Telekomunikasyon E.A.S. Cevizlibag Duragy, Yilanly Ayazma Yolu 14 Topkapi Istanbul, Turkey STANE SAKSIDA Institute of Sociology E. K. University of Ljubljana Cankarjeva ul. 1 61000 Ljubljana JERNEJ VIRANT Faculty of Electrical Engineering and Computing E. K. University of Ljubljana Tržaška c. 25 61000 Ljubljana Informatica is published four times a year in Winter, Spring, Summer and Autumn by the Slovene Society Informatika, Iskra Delta Computers, Stegne 15C, 61000 Ljubljana, Yugoslavia. A Journal of Computing and Informatics CONTENTS Synthesis in Complex Problem Domains An Informational Theory of Discourse I Assuring Numerical Stability in the Process of Matrbc Refactorization within Linear Programming Package on PC Formal Verification of Distributed Systems Characterization of Circuits in Grid Obtained by Regular and Semi - regular Tessellations On the Intersection of Two Convex Polygons Fractals - Science or Art (in Slovene) Application of Methods of Knowledge Engineereing in Education (in Serbo-Croatian) Strategy of Computing (in Slovene) News (in Slovene) Authors' Subject Index of the Journal Informatica, Volume 13 (1989) Some Recently Published Papers in Foreign Professional- Periodicals M. Gerkeš A. P. Železnikar J. Barle J. Grad Tatjana Kapus B. Horvat J. Žunić I. Stojmenović D. M. Acketa Violeta Hank D. Surla Jasna Donlagić N. Guid L. Jeremić Z. Budimac Mirjana Ivanović 1 16 j 38 44 48 52 58 69 72 82 92