- Email: [email protected]
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Slamecka, V. (1%6). Principles of substantive analysis of information. In Proc. of the 1965 Congress of the ht. Federation for Documentation, pp. 22!IL234. Spartan Books, Washington. Slamecka, V. (1973). An audiographic system for self-instruction. J. Am. Sot. Injorm. Sci. 24, 405415. Slamecka, V. and Pearson, C. (1975). Information science. In Encyclopedia of Computer Science (Ed. by A. Ralston and C. L. Meek). Petrocelli/Charter, New York. Slamecka, V. and Pearson, C. (1978). The portent of signs and symbols. In The Many Faces of Information Science (Ed. by E. Weiss), pp. 105-126. Westview Press, Boulder, Colorado. Stapleton, M. L. (1974). A Methodology Utilizing Semantic Information Measures for Conversational or Dialogue Experiments. Ph.D. Thesis. School of Information and Computer Science. Georgia Institute of Technology, Atlanta, Georgia. Ting, T. C. and Badre, A. N. (1975). Modelingco-adaptive man-machine interactive systems. In Proc. of the 1975 Southeastern Conj. of the Society for General Systems Research, Athens, Georgia. Ting, T. C. and Badre, A. N. (1976). Dynamic model of man-machine interactions: design and application with an audiographic learning facility. J. Man-machine Studies 8, 75-88. Ting. T. C. and Horng, C. S. (1975). Graphemic analysis and synthesis of Chinese ideograms. In Proc. of the 1975 Computer Science, Washington, D.C. Ting, T. C. and Horng, C. S. (1975a). Toward a systematic decomposition and automatic recomposition of Chinese ideographs. In Proc. of the 1975 Int. Computer Symp., Taipei, Republic of China. Valach, M. (1970). A Q-graph approach to parsing. In Proc. of the Conf. on Linguistics, University of Iowa. Winner, R. I. (1973). Cartoons: an initial investigation of animated graphs. In Proc. of the 1973 Annual Nat. Conf. of the ACM, Atlanta, Georgia. Zunde, P. (Ed.) (1974). Information Utilities: Proc. of the 37th Annual Meeting of the American Society of lnjormation Science, Atlanta, Georgia. Zunde. P. and Dexter, M. E. (1%8). Statistical models of index vocabularies. In J. Am. Sot. Inform. Sci. 5, 73-78.
3.
THEORY OF COMPUTATON
The School of Information and Computer Science has pursued an active program of research in theoretical computer science since 1968. The general orientation of its research program is metatheoretical-concerned more with unifying principles than with specific problems-and the directions taken by its researchers in the theory of computing have their basis in this milieu. Given this non-standard backdrop, the main lines of research at the School have paralleled national research interests; in several instances, however, our research results pre-date trends which later appear in the general literature. The specific contributions of the School’s researchers will be discussed under the following broad categories: (1) automata, forma1 languages, algorithms, complexity; (2) applications of logic to computer science; (3) new models of computation; and (4) current trends.
Automata, formal languages,
algorithms, complexity
Considerable development of the theory of systems of automata, arrayed in geometrical fashions, has taken place at the School between 1968 and 1976. One class of problems successfully addressed is the relationship between parallel and sequential nodes of operation of cellular arrays. An especially attractive by-product of these results is the ability to prove results concerning the processing of n-dimensional patterns (n 2 2). For definitions, let us consider a genera1 tessellation mode1 consisting of a countable set of uniform finite-state machines which are interconnected in some fashion which can be specified by a local neighborhood structure. Given the state of a machine M; and its neighbors N;, . . . , Nk, a local transformation determines the next state of Mi as a function of the k + 1 “local” states. A configuration of a tessellation automaton is defined by state description of the component machines. Parallel transformations update the configurations as follows: the state machine in a successor configuration of c is a function of the k + 1 states in configuration C* which differs from c only in that the states of all cells processed before c have been updated. Tessellation automaton TA simulates automaton TAT in (t/q) real-time if configurations reachable by q transformations in TA are reachable in at most t transformations in TA2. In (Grosky
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and Tsui, 1973), it is shown that, under suitable assumptions, (I) strictly parallel tessellation automata can simulate strictly sequential tessellation automata in (t/q) = 1 real-time; and, furthermore, (2) strictly sequential tessellation automata simulate strictly parallel tessellation automata in (t/q) = 2 real-time. Various combinations of sequential and parallel transformations are studied in (Grosky and Tsui, 1973a). These results are then related to the processing of “patterns”, i.e. fixed tessellations of the Euclidean plane and hyperplanes. By considering tessellations of other surfaces (i.e. nonuniform neighborhood interconnections), a surprising result can be proved. In 1973, Grosky and Tsui proved the existence of nonuniform complete one dimensional cellular arrays of every scope n 2 2: in particular, any pattern in these machines can be made to evolve from any other, improving a result of Amoroso and Yamada and Yamada and showing an increase in computational power through the introduction of nonuniformities. In (Wang and Grosky, 1975), a relationship is established between uniformly-structured machines and parallel array grammars. Contributions which significantly extend this theory are listed in the bibliography. In the area of machine-based complexity, much of the interest has centered around the computational power of non-standard machine models, and with developing conditions for existence of universal machines. Let M be a fixed automaton specified by its input alphabet X, finite-state transition table and auxiliary storage medium. By ‘f(M), we mean the set of input tapes (strings) “accepted” by M. We let u be a fixed function for encoding descriptions of automata into 2; in addition, suppose $ is a marker, $6? 2. Then a machine U is said to be universal over a class C of machines whenever MEC
u(M)$xE T(U) < = >
x E T(M).
Deimel (1975) examined the computational power of several variants of the (one-tape) Turing machine model; these results extended similar results by P. C. Fischer. We define the following types of Turing machines. A restricted machine of any type is one that moves its head on each quadruple. A DM is a Turing machine that, on each quadruple, changes state or prints a symbol, but not both. There are two positive results concerning these models. First, every restricted Turing machine with end markers can be simulated by a restricted DM. Second, there is a universal (for Turing machines) restricted Turing machine. However, if the simulation is required to be step-by-step, then there is a restricted Turing machine which cannot be simulated by any restricted DM. Gwynn and Martin in a series of papers (1973, 1974, 1975) examined the effects of varying heads and auxiliary storage for a variety of models. We use the notation in NPDA(k) in DSA(k) to represent, respectively, the classes of languages accepted by m-way non-deterministic pushown automata with k stores and m-way deterministic non-varying stack automata with k stores. Similar connections hold for related machines. Since the “determinism versus nondeterminism” problems seem rather difficult in general, Gwynn and Martin obtain rather less ambitious results concerning the gain in computational power afforded by varying resources available for the computations. For instance, they note that there is no INPDA which is universal for finite automata, but they show that there is a ZDPDA which is universal for finite automata. Similar results are used to classify multihead stack automata (SA) as follows: V n 2 2. The following classes contain universal machines over that class: 2DSA(n) 2NSA(n) 2DNESA(n)_Note: 2NNESA(n)
An NESA in non-erasing.
This final result we mention has to do with the power of DPDAs. It is known that 2NPDA(l)JDPDA(13); in particular, every context-free language is recognized by some deterministic two-way 13-head PDA. If the number of heads can be significantly reduced, then IPM Vol. 14 No. 54
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light is shed in the NPDA and 2DPDA classes since they are incomparable if 2DPDA(l) does not cover all context-free languages. In (Gwynn and Martin, 1975), the situation is cleared up somewhat by showing that two heads are sufficient to recognize all of the linear languages by 2DPDAs. Whether one is sufficient is still not known. In the area of algorithms and complexity, much of the work at the School has occurred only recently, and we reserve a special section for recent trends. However, we mention here two papers which are indicative of early efforts at the School in this area. Dunham (1970) considers a sieve method for generating the so-called complex primes; i.e. irreducible complex numbers (Y+ Pi where a, p E C. The efficiency of the procedure is tied to the following relationship between complex primality and integral primality: y E C is prime if (Iyl*, [By,, = 1 where .zo runs through all complex primes (y). In other work, Baralt-Torrijos and Pass (1969) anticipate later work in object code optimization in their method for Decision Table minimization; the key to this method lies in the viewing of the action of a decision table as a finite lattice to which Boolean function optimization techniques can be applied. Applications of logic to computer science We discuss in this section two fruitful lines of research which use common methods: the application of methods of mathematical logic to the problems of computer science. First, we will deal with the application of model-theoretic and other semantic methods to problems of programming languages. The following problems were considered (DeMillo, 1972). Let P be a set of “programs” formulated in a systematic way using first order formulas, terms and variables; the formalization of P should be sufficient to determine a method for interpreting the elements of P in a relational structure I?. Let @ be a class of properties of interpreted programs (e.g. termination, divergence,. . .) and write (19,@)I = p when p E P satifies property 0 in 6. Using the obvious analogy to bivalent propositional satisfaction, determine properties of 0 and of P which ensure that a “logic” for @ and P will exist. By “logic” we mean here an enumeration of p’s which have the property (8, @)I = p for all admissible 8. A natural question is under what conditions the logic for P has classical consistency and completeness theorems. This is rephrased as a question concerning the algebraic structure of P under a certain congruence relation induced by (6, @)I = . Two sufficient conditions are derived; P possesses a classical inferential structure if (1) P consists only of “propositional” (2) P solves its own halting problem.
programs, or
A contemporary reincarnation of (2) is that P must contain its own “assertion language”. The resulting theorem is thus closely related to Cook-style completeness for Hoare systems. Some technical details of inductively expressing the relation (19,@)I = were considered, together with a discussion of the pragmatic significance of such semantic evaluation (Chiaraviglio and Winner. 1975). In (Chiaraviglio, Baralt-Torrijos and Grosky, 1973, the language P consists of a fixed, first-order applicative system of combinatory logic, and for programs PO,p, the goal is to relate formulas of the form “p. = pI” to properties of (8, +)I = p. and (8, @)I = pI. It is shown for the class {Q} of formulas of the form “pi = pi”. The goal is to place some restrictions on the notions of “execution” of programs pi and “co-success” of pi, pj relative to @, so that a relation E(. , .) holds exactly when both pi, pi co-succeed in 6. A sort of completeness theorem is proved which relates a calculus for (4) to the relation E(. , .). In (Winner, 1975), these methods are carried to an even wider class of programs he calls PLi. His main concern is with a subclass L, of PL. Again, the formulas to be referentially interpreted are of the form “p. = p,“. Winner’s main results first establish a soundness theorem for the referential semantics. More importantly, Winner also proves a relative completeness theorem for his language. The main thrust of these studies concluded in 1975, but it is important to note that in several respects they presaged current interest in “programmatic logics”. Indeed, the bulk of the initial set of results by Cook and others were hinted at in the School’s research carried out from 1%8 to 1975.
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A second, unrelated program in applying logical methods to computer science used, from 1972 through 1976, the methods and results of combinatory logic to simplify certain problems in automata theory. In (Grosky, 1972), it is shown how to construct a system of combinatory logic to describe systems of automata. The construction is made complicated by the restriction that if A0 is an n input machine represented by the formula a0 and A,, . . . , A, are represented by al,. . . , a., then ao(a,, . . , a,) should be well-formed just in case all ai(i > 0) are legal inputs to Ao. Some advantages of such a construction are exhibited. It is shown, for instance, that the class of machines {A;} can be partitioned into “complexity” classes by operations in the representing system {ai}. New models of computation Several of the results discussed above grew out of technical problems arising in the School’s attempts to construct new models of computation. This research effort was conceived in early 1969, at a time when there was considerable concern over the rapidly proliferating computational models. This was a watershed period; there was still considerable uncertainty over the stability of the various models of computation, and it was perceived that perhaps unifying structure might be imposed upon the apparent disarray by devising a single model of computation with rich enough mathematical structure to mirror important classifications of machines. In the School’s effort, the initial attempts were combinatorial and algebraic. A rather thorough attempt was made to “define” essential computational ideas as combinators in a system of combinatory logic (Poore, Baralt-Torrijos and Chiaraviglio, 1971). The method is indirect: First, it is shown how to reassemble the finitary actions of an abstractly construed computing device as functions of a product Boolean algebra of the form (0”)’ where 0 = (0,1) is the simple finite Boolean algebra. The second stage of this process then involved representing functions in (on)lr as “bit string” where “bits” are taken to be combinators in a system of combinatory logic H’. Thus, “words” of memory are wffs over {I, 0). for example. Since combinators in H’ are applicative objects, there is nothing to guarantee that a “word” is its own normal form; so, a blocking operator is used to ensure the uniqueness of memory states. The bulk of the paper is taken up with showing that all Boolean functions can be mirrored by transitions between wffs in H’. That such a unique representation exists is called the Hardware Definability Theorem. By conceiving of data structures as sets of states and letting computations be specified by their actions on data structures, a Software Definability Theorem is obtained by similar techniques. Poore (1970) noticed that the passage to combinatory representation is not required and so began to request the above model in a purely algebraic way. Following the general outline given by Halmos, Poore sought to place the major models of computation within the setting of algebraic logic: i.e. he sought to define the major machine models as Boolean algebras with operators. To this end, a computation algebra is developed. A computation algebra is a Boolean algebra with two types of operators, transformation and resets. Transformations are Boolean endomorphisms on the algebra, induced by transformations on an index set. These are the transformations of Halmos’ polyadic algebras. Reset operators are essentially normed, additive, multiplicative and idempotent hemimorphisms on the algebra. It is also required that each reset operator be obtainable from a distinguished element of the algebra and a transformation. Results obtained are as follows. Every hardware structure can be coded into a larger hardware structure in which the operations are mirrored in hemimorphisms, or into a still larger hardware structure in which the operations are mirrored in Boolean endomorphisms (transformations). These codings are not morphisms. Every finite computer can be coded into one universal computer by a function which is not necessarily a morphism, where a universal computer is a computation algebra together with a control unit which has the closure of the resets and transformations under functional composition for its range. Every computer is the quotient of some universal computer. The universal algebraic concepts are developed for computational algebras. Both a hemomorphism theorem and a representatation theorem are stated and proved. This theory of morphisms is then extended to computers. Following the theory of Boolean duality, the notion
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of a computation space is developed. At this point in the development, contact is made with the theory of polyadic algebras. Computation algebras differ from polyadic algebras in that whereas the former has reset operators, the latter has quantifier operators. However, the duals of both types of operators are Boolean relations, since they are both homomorphisms. The present work falls within the province of Boolean algebras with operators; thus Tarski’s general representation theorem for such algebras is available for computation algebras. In (Roehrkasse, 1971; Roehrkasse and Chiaraviglio, 1972; and Horgan, Roehrkasse and Chiaraviglio, 1972), Poore’s model was defined to reflect the linear structure of resource constrained computational devices; i.e. the various subrecursive automata classes. In Roehrkasse, for example, an attempt was made to recover the Chomsky hierarchy of languages and machines in a strictly algebraic way: by classifying morphisms between the algebras representing these machines. Horgan’s thesis is an interesting sidelight in this research: he attempts to extend the theory algebraically to recover super-recursive computation. Specifically, he shows how relative computation could be employed in the algebraic setting so that algebraic structural similarity parallels the degrees of unsolvability. Current trends The School’s efforts in the theoretical computer science have recently taken on a different character. We discuss two research areas in which current research is being performed. In (Lipton, Eisenstat and DeMillo, 1976) the following combinatorial relation was introduced. Let G and G* be directed graphs with vertex sets V( ) and arc sets A(.). Let d be the distance metric on graphs. Say G 5 s,TG* if there is a @ : V(G*)+ V(G); such that 0 5 ((I-‘(X*) < S for all x E V(G*) and for all x* E V(G) if @(x)=x* and (x,y) E A(G), then for some @(y*) = y, dc+(x*, y) 1. T. In other words, G I aTG* if it is possible to embed G into G* by dilating paths by at most a factor of T, providing the vertex is split more than S times. A first application is a space-time tradeoff for structured programs. In (Lipton, Eisenstat and DeMillo, 1976), it is shown that every n statement go-to program can be simulated by some “structure” program providing only that the structured program be S times larger and T times slower, where T + log,log, S 1 log, n. The combinatorial lemmas in which this rests can be used to determine worst-case and average-case rates of growth for certain data structuring problems. For example, if G, is an n x n array and G is a specific graph, we may want to know that G. can be “stored” as G with loss of logical proximity T; i.e. G, 5 ,.TG. But if G is a binary tree, then T 2 log,n - O(1). The same technique answers about universal data structures. universal for binary n-trees if for all binary trees G we have
If T is worst-case
Say that a binary
tree H is
then
‘But if T is averaged over all edges the H can be quite small: if G <(l/a)H by average loss of proximity l/a then H = O(n’Os(s+n))is achievable. One research effort at the School is the study of the relative aspects of computational complexity. This general area of study had its roots in recursive function theory, Turing computability theory and abstract complexity theory. Thus, early results tended to be general and to make statements primarily applicable at high levels of complexity. Work of Cook, Karp and many followers, on reducibilities between combinatorial problems, spurred the exploration of relative aspects of complexity at an intermediate (polynomial) level. But only recently has it
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been noticed that relative complexity can also be a unifying concept for lower level “concrete” complexity theory. This point of view accords very well with a modular philosophy of program design, verification and analysis. In (Lynch and Blum, 1977 and Lynch, 1978), definitions for computability and complexity of one algebra relative to another are proposed. The basic definition requires that each element of the desired algebra have at least one representation as an element of the given algebra, and that each basic operation of the desired algebra have a program (a flowchart, for example) over the basic operations of the given algebra. The definition is surprisingly similar to those in (Lipton, Eisenstat and DeMillo, 1976); relative codings of algebras are treated in a way very similar to the way relative codings of data structures and control structures are treated in that other effort. The naturalness of the new definition is further supported by the simplicity of its algebraic properties and by its usefulness for proving several clusters of technical results about relative complexity of specific algebras. For example, it is proved that certain common algebras with numerical or bit string domains have or do not have inherent power of “efficient computation”; efficient reducibilities between some of these algebras allow the results for some algebras to be inferred from those for others. As another example, results are proved which can be interpreted as saying that certain relative codings of simple algebras are optimal. Dependency of results on the choice of class of programs is also discussed. REFERENCES Baralt-Torrijos, J. and Pass, E. M. (1969). Decision table minimization. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Chiaraviglio, L., Baralt-Torrijos, J. and Grosky, W. (1975). The programmatic semantics of binary predicator calculi. The Notre Dame J. Formal Logic XVI(6), 591-5%. Chiaraviglio, L. and Winner, I. R. (1975). Programming valuation spaces. In Proc. of the 5th In?. Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada. Cooper, R. V. (1973). Derivation from queueing theory of an identity related to Abel’s generalization of the binomial theorem, which is useful in graph theory. Management Sci. 19, 582-584. Deimel, I. E., Jr. (1975). Remark on the computational power of a turing machine variant. Inform. Proc. Lett. 3, 43-45. Deimel, I. E., Jr. (1975a). Automata networks and new counter machine hierarchy. In Proc. of the 1975 Association for Computing Machinery Computer Science Conf., Washington, DC. DeMillo, R.AA. (1971). Formal Semantics and the Logical Structure of Programming Languages. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. DeMiIlo, and Chiaraviglio, L. (1972). On the applicative nature of assignment. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. DeMillo, R., Eisenstat, S. and Lipton, R. Preserving average proximity in arrays. Commun. ACM. to be published. Dunham, K. B. (1970). An algorithm to produce complex primes. Commun. ACM 13(l), 52-55. Grosky, W. (1972). Universal tessellation automata: an application of combinatory logic to automata theory. In Proc. of the 10th Annual Allerton Conf. on Circuit and System Theory, Monticello, Illinois. Grosky, W. I. (1974). Stratified combinatory logic of fixed applicative scope: applications to automata which compute and construct. J. Symbolic Logic 39, 376-377. Grosky, W. (1976). Real-time multi-counter automata networks. Paper presented at the 1976 Conf. on Information Sciences and Systems, Baltimore, Maryland. Grosky, W. I. and Tsui, F. (1973). Parallel-sequential processing of finite patterns. In Proc. of the Znt.Symp. on Computers and Chinesell Systems; also in Proc. of the 1973 Sagamore Conf. on ParallelProcessing, Syracuse, New York. Grosky, W. I. and Tsui, F. (1973). Pattern generation in non-standard tessellation automata. In Proc. of the 1973 ACM Conf., Atlanta, Georgia. Grosky, W. I. and Tsui, F. (1973). Evolution of patterns in cellular structures with nonuniform parallel transformations. In Proc. of the 1973 IEEE Systems, Man and Cybernetics Conf., Boston, Mass. Grosky, W. and Wang, S. P. (1975). The relation between uniformly structured tessellation automata and parallel array grammars. In Proc. of the Int. Symp. on Uniformly Structured Automata and Logic, Tokyo, Japan. Grosky, W. I. and Wang, S. P. (1975a). SIMPARAG-Simultaneous parallel array grammar. In Proc. of the 4th Sagamore Computer Conf. on Parallel Processing, Syracuse, New York.
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Gwynn. J. M. and Martin, D. P. (1973). Two results concerning the power of two-way deterministic push down automata. In Proc. of the 1973 ACM Nat. Conf., Atlanta, Georgia. Gwynn, J. M. and Martin, D. P. (1975). Deterministic parsing of (minimal) linear languages. In Proc. of the 1975 Southeastern Symp. on System Theory, Tuskegee, Alabama. Gwynn, J. M. and Martin, D. P. (1975a). Universal multihead stack automata. In Proc. of the 1975 Southeastern Symp. on System Theory, Tuskegee, Alabama. Horgan. J. R. (1972). Abstract Computers and Degrees of Unsolvability. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Horgan. J. R., Roehrkasse, R. C. and Chiaraviglio, L. (1972). Abstract digital computers and Turing machines. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Lipton, R., Eisenstat, S. and DeMillo, R. (1976). Space and time hierarchies for classes of control and data structures. J. ACM 23(4), 720-732. Lynch, N. and Blum, E. (1978). Straight-line program length as a parameter for complexity measure. In Proc. of the SIGACT Symp. 1978. Lynch, N. and Blum, E. (1977). Efficient reducibility between programming systems. In Proc. of the SIGACT Symp. 1977. Martin, D. P. (1974) Universal Multihead Automata. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Poore. J. H., Jr. (1969). An Algebraic Theory of the Syntax of Programming Languages. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Poore, J. H.. Jr. (1970). Toward an Algebra of Computation. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Poore, J. H., Jr., Baralt-Torrijos. J. and Chiaraviglio, L. (1972). On the combinatory definability of hardware and software. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta. Georgia. Roehrkasse, R. C. (1971). Abstract Digital Computers and Automata. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Roehrkasse. R. C. and Chiaraviglio, L. (1972). An algebraic alter ego for the classical hierarchy of recognizers. Research report School of Information and Computer Science, Georgia Institute of Technology, Atlanta Georgia. Slamecka, V. and Gehl. J. M. (1972). Requirements for a data base management system. In Ideas for Management: Proc. of the 1972 Int. Systems Meeting, Miami, Florida. Slamecka. V., Zunde. P. and Dexter, M. E. (1970). Data Collection, organization and use. In Proc. of the 1970 Int. Systems Meeting, Las Vegas, Nevada. Tsui, F. (1974). Parallel and Sequential Operations with Array Processors. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Winner, R. I. (1975). Toward the primary logics of programming languages. In Proc. of the 1975 Association for Computing Machinery Computer Science Conf., Washington, DC. 4. THEORY
OF SYSTEMS
has been pointed out that the concept of a system is central to almost all areas of information processing and decision making. In general, the notion of a system is introduced to denote the existence of relationships between the data or variables that are observed, or more specifically the existence of a transformation of some set of data into another set. The notion of a system can in a certain sense be considered to be counterpart to the notion of a physical object; just as different physical theories deal with different kinds of physical objects, various aspects of information processing and decision making theories deal with various types of “systems” and their behavior, transformations, control, etc. The theory of information processing and decision making can be considered therefore to be a theory of systems. Of particular interest to this School have been aspects of system theory which are applicable to information system analysis and design. Theoretical research performed in this subject field will be presented under the following headings: theory of dynamical systems; modeling and simulation; and information system design. It
Theory of dynamical systems
Dynamical systems are of great theoretical and practical interest to information scientists. Of course deterministic automata form a subclass of these systems. One of the topics of the School’s research in this area has been the relation between controllability, observability and invariance as
Information sciences at Georgia Institute of Technology: the formative years 1%3-78
Slamecka, V. (1%6). Principles of substantive analysis of information. In Proc. of the 1965 Congress of the ht. Federation for Documentation, pp. 22!IL234. Spartan Books, Washington. Slamecka, V. (1973). An audiographic system for self-instruction. J. Am. Sot. Injorm. Sci. 24, 405415. Slamecka, V. and Pearson, C. (1975). Information science. In Encyclopedia of Computer Science (Ed. by A. Ralston and C. L. Meek). Petrocelli/Charter, New York. Slamecka, V. and Pearson, C. (1978). The portent of signs and symbols. In The Many Faces of Information Science (Ed. by E. Weiss), pp. 105-126. Westview Press, Boulder, Colorado. Stapleton, M. L. (1974). A Methodology Utilizing Semantic Information Measures for Conversational or Dialogue Experiments. Ph.D. Thesis. School of Information and Computer Science. Georgia Institute of Technology, Atlanta, Georgia. Ting, T. C. and Badre, A. N. (1975). Modelingco-adaptive man-machine interactive systems. In Proc. of the 1975 Southeastern Conj. of the Society for General Systems Research, Athens, Georgia. Ting, T. C. and Badre, A. N. (1976). Dynamic model of man-machine interactions: design and application with an audiographic learning facility. J. Man-machine Studies 8, 75-88. Ting. T. C. and Horng, C. S. (1975). Graphemic analysis and synthesis of Chinese ideograms. In Proc. of the 1975 Computer Science, Washington, D.C. Ting, T. C. and Horng, C. S. (1975a). Toward a systematic decomposition and automatic recomposition of Chinese ideographs. In Proc. of the 1975 Int. Computer Symp., Taipei, Republic of China. Valach, M. (1970). A Q-graph approach to parsing. In Proc. of the Conf. on Linguistics, University of Iowa. Winner, R. I. (1973). Cartoons: an initial investigation of animated graphs. In Proc. of the 1973 Annual Nat. Conf. of the ACM, Atlanta, Georgia. Zunde, P. (Ed.) (1974). Information Utilities: Proc. of the 37th Annual Meeting of the American Society of lnjormation Science, Atlanta, Georgia. Zunde. P. and Dexter, M. E. (1%8). Statistical models of index vocabularies. In J. Am. Sot. Inform. Sci. 5, 73-78.
3.
THEORY OF COMPUTATON
The School of Information and Computer Science has pursued an active program of research in theoretical computer science since 1968. The general orientation of its research program is metatheoretical-concerned more with unifying principles than with specific problems-and the directions taken by its researchers in the theory of computing have their basis in this milieu. Given this non-standard backdrop, the main lines of research at the School have paralleled national research interests; in several instances, however, our research results pre-date trends which later appear in the general literature. The specific contributions of the School’s researchers will be discussed under the following broad categories: (1) automata, forma1 languages, algorithms, complexity; (2) applications of logic to computer science; (3) new models of computation; and (4) current trends.
Automata, formal languages,
algorithms, complexity
Considerable development of the theory of systems of automata, arrayed in geometrical fashions, has taken place at the School between 1968 and 1976. One class of problems successfully addressed is the relationship between parallel and sequential nodes of operation of cellular arrays. An especially attractive by-product of these results is the ability to prove results concerning the processing of n-dimensional patterns (n 2 2). For definitions, let us consider a genera1 tessellation mode1 consisting of a countable set of uniform finite-state machines which are interconnected in some fashion which can be specified by a local neighborhood structure. Given the state of a machine M; and its neighbors N;, . . . , Nk, a local transformation determines the next state of Mi as a function of the k + 1 “local” states. A configuration of a tessellation automaton is defined by state description of the component machines. Parallel transformations update the configurations as follows: the state machine in a successor configuration of c is a function of the k + 1 states in configuration C* which differs from c only in that the states of all cells processed before c have been updated. Tessellation automaton TA simulates automaton TAT in (t/q) real-time if configurations reachable by q transformations in TA are reachable in at most t transformations in TA2. In (Grosky
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and Tsui, 1973), it is shown that, under suitable assumptions, (I) strictly parallel tessellation automata can simulate strictly sequential tessellation automata in (t/q) = 1 real-time; and, furthermore, (2) strictly sequential tessellation automata simulate strictly parallel tessellation automata in (t/q) = 2 real-time. Various combinations of sequential and parallel transformations are studied in (Grosky and Tsui, 1973a). These results are then related to the processing of “patterns”, i.e. fixed tessellations of the Euclidean plane and hyperplanes. By considering tessellations of other surfaces (i.e. nonuniform neighborhood interconnections), a surprising result can be proved. In 1973, Grosky and Tsui proved the existence of nonuniform complete one dimensional cellular arrays of every scope n 2 2: in particular, any pattern in these machines can be made to evolve from any other, improving a result of Amoroso and Yamada and Yamada and showing an increase in computational power through the introduction of nonuniformities. In (Wang and Grosky, 1975), a relationship is established between uniformly-structured machines and parallel array grammars. Contributions which significantly extend this theory are listed in the bibliography. In the area of machine-based complexity, much of the interest has centered around the computational power of non-standard machine models, and with developing conditions for existence of universal machines. Let M be a fixed automaton specified by its input alphabet X, finite-state transition table and auxiliary storage medium. By ‘f(M), we mean the set of input tapes (strings) “accepted” by M. We let u be a fixed function for encoding descriptions of automata into 2; in addition, suppose $ is a marker, $6? 2. Then a machine U is said to be universal over a class C of machines whenever MEC
u(M)$xE T(U) < = >
x E T(M).
Deimel (1975) examined the computational power of several variants of the (one-tape) Turing machine model; these results extended similar results by P. C. Fischer. We define the following types of Turing machines. A restricted machine of any type is one that moves its head on each quadruple. A DM is a Turing machine that, on each quadruple, changes state or prints a symbol, but not both. There are two positive results concerning these models. First, every restricted Turing machine with end markers can be simulated by a restricted DM. Second, there is a universal (for Turing machines) restricted Turing machine. However, if the simulation is required to be step-by-step, then there is a restricted Turing machine which cannot be simulated by any restricted DM. Gwynn and Martin in a series of papers (1973, 1974, 1975) examined the effects of varying heads and auxiliary storage for a variety of models. We use the notation in NPDA(k) in DSA(k) to represent, respectively, the classes of languages accepted by m-way non-deterministic pushown automata with k stores and m-way deterministic non-varying stack automata with k stores. Similar connections hold for related machines. Since the “determinism versus nondeterminism” problems seem rather difficult in general, Gwynn and Martin obtain rather less ambitious results concerning the gain in computational power afforded by varying resources available for the computations. For instance, they note that there is no INPDA which is universal for finite automata, but they show that there is a ZDPDA which is universal for finite automata. Similar results are used to classify multihead stack automata (SA) as follows: V n 2 2. The following classes contain universal machines over that class: 2DSA(n) 2NSA(n) 2DNESA(n)_Note: 2NNESA(n)
An NESA in non-erasing.
This final result we mention has to do with the power of DPDAs. It is known that 2NPDA(l)JDPDA(13); in particular, every context-free language is recognized by some deterministic two-way 13-head PDA. If the number of heads can be significantly reduced, then IPM Vol. 14 No. 54
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light is shed in the NPDA and 2DPDA classes since they are incomparable if 2DPDA(l) does not cover all context-free languages. In (Gwynn and Martin, 1975), the situation is cleared up somewhat by showing that two heads are sufficient to recognize all of the linear languages by 2DPDAs. Whether one is sufficient is still not known. In the area of algorithms and complexity, much of the work at the School has occurred only recently, and we reserve a special section for recent trends. However, we mention here two papers which are indicative of early efforts at the School in this area. Dunham (1970) considers a sieve method for generating the so-called complex primes; i.e. irreducible complex numbers (Y+ Pi where a, p E C. The efficiency of the procedure is tied to the following relationship between complex primality and integral primality: y E C is prime if (Iyl*, [By,, = 1 where .zo runs through all complex primes (y). In other work, Baralt-Torrijos and Pass (1969) anticipate later work in object code optimization in their method for Decision Table minimization; the key to this method lies in the viewing of the action of a decision table as a finite lattice to which Boolean function optimization techniques can be applied. Applications of logic to computer science We discuss in this section two fruitful lines of research which use common methods: the application of methods of mathematical logic to the problems of computer science. First, we will deal with the application of model-theoretic and other semantic methods to problems of programming languages. The following problems were considered (DeMillo, 1972). Let P be a set of “programs” formulated in a systematic way using first order formulas, terms and variables; the formalization of P should be sufficient to determine a method for interpreting the elements of P in a relational structure I?. Let @ be a class of properties of interpreted programs (e.g. termination, divergence,. . .) and write (19,@)I = p when p E P satifies property 0 in 6. Using the obvious analogy to bivalent propositional satisfaction, determine properties of 0 and of P which ensure that a “logic” for @ and P will exist. By “logic” we mean here an enumeration of p’s which have the property (8, @)I = p for all admissible 8. A natural question is under what conditions the logic for P has classical consistency and completeness theorems. This is rephrased as a question concerning the algebraic structure of P under a certain congruence relation induced by (6, @)I = . Two sufficient conditions are derived; P possesses a classical inferential structure if (1) P consists only of “propositional” (2) P solves its own halting problem.
programs, or
A contemporary reincarnation of (2) is that P must contain its own “assertion language”. The resulting theorem is thus closely related to Cook-style completeness for Hoare systems. Some technical details of inductively expressing the relation (19,@)I = were considered, together with a discussion of the pragmatic significance of such semantic evaluation (Chiaraviglio and Winner. 1975). In (Chiaraviglio, Baralt-Torrijos and Grosky, 1973, the language P consists of a fixed, first-order applicative system of combinatory logic, and for programs PO,p, the goal is to relate formulas of the form “p. = pI” to properties of (8, +)I = p. and (8, @)I = pI. It is shown for the class {Q} of formulas of the form “pi = pi”. The goal is to place some restrictions on the notions of “execution” of programs pi and “co-success” of pi, pj relative to @, so that a relation E(. , .) holds exactly when both pi, pi co-succeed in 6. A sort of completeness theorem is proved which relates a calculus for (4) to the relation E(. , .). In (Winner, 1975), these methods are carried to an even wider class of programs he calls PLi. His main concern is with a subclass L, of PL. Again, the formulas to be referentially interpreted are of the form “p. = p,“. Winner’s main results first establish a soundness theorem for the referential semantics. More importantly, Winner also proves a relative completeness theorem for his language. The main thrust of these studies concluded in 1975, but it is important to note that in several respects they presaged current interest in “programmatic logics”. Indeed, the bulk of the initial set of results by Cook and others were hinted at in the School’s research carried out from 1%8 to 1975.
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A second, unrelated program in applying logical methods to computer science used, from 1972 through 1976, the methods and results of combinatory logic to simplify certain problems in automata theory. In (Grosky, 1972), it is shown how to construct a system of combinatory logic to describe systems of automata. The construction is made complicated by the restriction that if A0 is an n input machine represented by the formula a0 and A,, . . . , A, are represented by al,. . . , a., then ao(a,, . . , a,) should be well-formed just in case all ai(i > 0) are legal inputs to Ao. Some advantages of such a construction are exhibited. It is shown, for instance, that the class of machines {A;} can be partitioned into “complexity” classes by operations in the representing system {ai}. New models of computation Several of the results discussed above grew out of technical problems arising in the School’s attempts to construct new models of computation. This research effort was conceived in early 1969, at a time when there was considerable concern over the rapidly proliferating computational models. This was a watershed period; there was still considerable uncertainty over the stability of the various models of computation, and it was perceived that perhaps unifying structure might be imposed upon the apparent disarray by devising a single model of computation with rich enough mathematical structure to mirror important classifications of machines. In the School’s effort, the initial attempts were combinatorial and algebraic. A rather thorough attempt was made to “define” essential computational ideas as combinators in a system of combinatory logic (Poore, Baralt-Torrijos and Chiaraviglio, 1971). The method is indirect: First, it is shown how to reassemble the finitary actions of an abstractly construed computing device as functions of a product Boolean algebra of the form (0”)’ where 0 = (0,1) is the simple finite Boolean algebra. The second stage of this process then involved representing functions in (on)lr as “bit string” where “bits” are taken to be combinators in a system of combinatory logic H’. Thus, “words” of memory are wffs over {I, 0). for example. Since combinators in H’ are applicative objects, there is nothing to guarantee that a “word” is its own normal form; so, a blocking operator is used to ensure the uniqueness of memory states. The bulk of the paper is taken up with showing that all Boolean functions can be mirrored by transitions between wffs in H’. That such a unique representation exists is called the Hardware Definability Theorem. By conceiving of data structures as sets of states and letting computations be specified by their actions on data structures, a Software Definability Theorem is obtained by similar techniques. Poore (1970) noticed that the passage to combinatory representation is not required and so began to request the above model in a purely algebraic way. Following the general outline given by Halmos, Poore sought to place the major models of computation within the setting of algebraic logic: i.e. he sought to define the major machine models as Boolean algebras with operators. To this end, a computation algebra is developed. A computation algebra is a Boolean algebra with two types of operators, transformation and resets. Transformations are Boolean endomorphisms on the algebra, induced by transformations on an index set. These are the transformations of Halmos’ polyadic algebras. Reset operators are essentially normed, additive, multiplicative and idempotent hemimorphisms on the algebra. It is also required that each reset operator be obtainable from a distinguished element of the algebra and a transformation. Results obtained are as follows. Every hardware structure can be coded into a larger hardware structure in which the operations are mirrored in hemimorphisms, or into a still larger hardware structure in which the operations are mirrored in Boolean endomorphisms (transformations). These codings are not morphisms. Every finite computer can be coded into one universal computer by a function which is not necessarily a morphism, where a universal computer is a computation algebra together with a control unit which has the closure of the resets and transformations under functional composition for its range. Every computer is the quotient of some universal computer. The universal algebraic concepts are developed for computational algebras. Both a hemomorphism theorem and a representatation theorem are stated and proved. This theory of morphisms is then extended to computers. Following the theory of Boolean duality, the notion
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of a computation space is developed. At this point in the development, contact is made with the theory of polyadic algebras. Computation algebras differ from polyadic algebras in that whereas the former has reset operators, the latter has quantifier operators. However, the duals of both types of operators are Boolean relations, since they are both homomorphisms. The present work falls within the province of Boolean algebras with operators; thus Tarski’s general representation theorem for such algebras is available for computation algebras. In (Roehrkasse, 1971; Roehrkasse and Chiaraviglio, 1972; and Horgan, Roehrkasse and Chiaraviglio, 1972), Poore’s model was defined to reflect the linear structure of resource constrained computational devices; i.e. the various subrecursive automata classes. In Roehrkasse, for example, an attempt was made to recover the Chomsky hierarchy of languages and machines in a strictly algebraic way: by classifying morphisms between the algebras representing these machines. Horgan’s thesis is an interesting sidelight in this research: he attempts to extend the theory algebraically to recover super-recursive computation. Specifically, he shows how relative computation could be employed in the algebraic setting so that algebraic structural similarity parallels the degrees of unsolvability. Current trends The School’s efforts in the theoretical computer science have recently taken on a different character. We discuss two research areas in which current research is being performed. In (Lipton, Eisenstat and DeMillo, 1976) the following combinatorial relation was introduced. Let G and G* be directed graphs with vertex sets V( ) and arc sets A(.). Let d be the distance metric on graphs. Say G 5 s,TG* if there is a @ : V(G*)+ V(G); such that 0 5 ((I-‘(X*) < S for all x E V(G*) and for all x* E V(G) if @(x)=x* and (x,y) E A(G), then for some @(y*) = y, dc+(x*, y) 1. T. In other words, G I aTG* if it is possible to embed G into G* by dilating paths by at most a factor of T, providing the vertex is split more than S times. A first application is a space-time tradeoff for structured programs. In (Lipton, Eisenstat and DeMillo, 1976), it is shown that every n statement go-to program can be simulated by some “structure” program providing only that the structured program be S times larger and T times slower, where T + log,log, S 1 log, n. The combinatorial lemmas in which this rests can be used to determine worst-case and average-case rates of growth for certain data structuring problems. For example, if G, is an n x n array and G is a specific graph, we may want to know that G. can be “stored” as G with loss of logical proximity T; i.e. G, 5 ,.TG. But if G is a binary tree, then T 2 log,n - O(1). The same technique answers about universal data structures. universal for binary n-trees if for all binary trees G we have
If T is worst-case
Say that a binary
tree H is
then
‘But if T is averaged over all edges the H can be quite small: if G <(l/a)H by average loss of proximity l/a then H = O(n’Os(s+n))is achievable. One research effort at the School is the study of the relative aspects of computational complexity. This general area of study had its roots in recursive function theory, Turing computability theory and abstract complexity theory. Thus, early results tended to be general and to make statements primarily applicable at high levels of complexity. Work of Cook, Karp and many followers, on reducibilities between combinatorial problems, spurred the exploration of relative aspects of complexity at an intermediate (polynomial) level. But only recently has it
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been noticed that relative complexity can also be a unifying concept for lower level “concrete” complexity theory. This point of view accords very well with a modular philosophy of program design, verification and analysis. In (Lynch and Blum, 1977 and Lynch, 1978), definitions for computability and complexity of one algebra relative to another are proposed. The basic definition requires that each element of the desired algebra have at least one representation as an element of the given algebra, and that each basic operation of the desired algebra have a program (a flowchart, for example) over the basic operations of the given algebra. The definition is surprisingly similar to those in (Lipton, Eisenstat and DeMillo, 1976); relative codings of algebras are treated in a way very similar to the way relative codings of data structures and control structures are treated in that other effort. The naturalness of the new definition is further supported by the simplicity of its algebraic properties and by its usefulness for proving several clusters of technical results about relative complexity of specific algebras. For example, it is proved that certain common algebras with numerical or bit string domains have or do not have inherent power of “efficient computation”; efficient reducibilities between some of these algebras allow the results for some algebras to be inferred from those for others. As another example, results are proved which can be interpreted as saying that certain relative codings of simple algebras are optimal. Dependency of results on the choice of class of programs is also discussed. REFERENCES Baralt-Torrijos, J. and Pass, E. M. (1969). Decision table minimization. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Chiaraviglio, L., Baralt-Torrijos, J. and Grosky, W. (1975). The programmatic semantics of binary predicator calculi. The Notre Dame J. Formal Logic XVI(6), 591-5%. Chiaraviglio, L. and Winner, I. R. (1975). Programming valuation spaces. In Proc. of the 5th In?. Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada. Cooper, R. V. (1973). Derivation from queueing theory of an identity related to Abel’s generalization of the binomial theorem, which is useful in graph theory. Management Sci. 19, 582-584. Deimel, I. E., Jr. (1975). Remark on the computational power of a turing machine variant. Inform. Proc. Lett. 3, 43-45. Deimel, I. E., Jr. (1975a). Automata networks and new counter machine hierarchy. In Proc. of the 1975 Association for Computing Machinery Computer Science Conf., Washington, DC. DeMillo, R.AA. (1971). Formal Semantics and the Logical Structure of Programming Languages. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. DeMiIlo, and Chiaraviglio, L. (1972). On the applicative nature of assignment. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. DeMillo, R., Eisenstat, S. and Lipton, R. Preserving average proximity in arrays. Commun. ACM. to be published. Dunham, K. B. (1970). An algorithm to produce complex primes. Commun. ACM 13(l), 52-55. Grosky, W. (1972). Universal tessellation automata: an application of combinatory logic to automata theory. In Proc. of the 10th Annual Allerton Conf. on Circuit and System Theory, Monticello, Illinois. Grosky, W. I. (1974). Stratified combinatory logic of fixed applicative scope: applications to automata which compute and construct. J. Symbolic Logic 39, 376-377. Grosky, W. (1976). Real-time multi-counter automata networks. Paper presented at the 1976 Conf. on Information Sciences and Systems, Baltimore, Maryland. Grosky, W. I. and Tsui, F. (1973). Parallel-sequential processing of finite patterns. In Proc. of the Znt.Symp. on Computers and Chinesell Systems; also in Proc. of the 1973 Sagamore Conf. on ParallelProcessing, Syracuse, New York. Grosky, W. I. and Tsui, F. (1973). Pattern generation in non-standard tessellation automata. In Proc. of the 1973 ACM Conf., Atlanta, Georgia. Grosky, W. I. and Tsui, F. (1973). Evolution of patterns in cellular structures with nonuniform parallel transformations. In Proc. of the 1973 IEEE Systems, Man and Cybernetics Conf., Boston, Mass. Grosky, W. and Wang, S. P. (1975). The relation between uniformly structured tessellation automata and parallel array grammars. In Proc. of the Int. Symp. on Uniformly Structured Automata and Logic, Tokyo, Japan. Grosky, W. I. and Wang, S. P. (1975a). SIMPARAG-Simultaneous parallel array grammar. In Proc. of the 4th Sagamore Computer Conf. on Parallel Processing, Syracuse, New York.
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Gwynn. J. M. and Martin, D. P. (1973). Two results concerning the power of two-way deterministic push down automata. In Proc. of the 1973 ACM Nat. Conf., Atlanta, Georgia. Gwynn, J. M. and Martin, D. P. (1975). Deterministic parsing of (minimal) linear languages. In Proc. of the 1975 Southeastern Symp. on System Theory, Tuskegee, Alabama. Gwynn, J. M. and Martin, D. P. (1975a). Universal multihead stack automata. In Proc. of the 1975 Southeastern Symp. on System Theory, Tuskegee, Alabama. Horgan. J. R. (1972). Abstract Computers and Degrees of Unsolvability. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Horgan. J. R., Roehrkasse, R. C. and Chiaraviglio, L. (1972). Abstract digital computers and Turing machines. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Lipton, R., Eisenstat, S. and DeMillo, R. (1976). Space and time hierarchies for classes of control and data structures. J. ACM 23(4), 720-732. Lynch, N. and Blum, E. (1978). Straight-line program length as a parameter for complexity measure. In Proc. of the SIGACT Symp. 1978. Lynch, N. and Blum, E. (1977). Efficient reducibility between programming systems. In Proc. of the SIGACT Symp. 1977. Martin, D. P. (1974) Universal Multihead Automata. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Poore. J. H., Jr. (1969). An Algebraic Theory of the Syntax of Programming Languages. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Poore, J. H.. Jr. (1970). Toward an Algebra of Computation. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Poore, J. H., Jr., Baralt-Torrijos. J. and Chiaraviglio, L. (1972). On the combinatory definability of hardware and software. Research Rep. School of Information and Computer Science, Georgia Institute of Technology, Atlanta. Georgia. Roehrkasse, R. C. (1971). Abstract Digital Computers and Automata. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Roehrkasse. R. C. and Chiaraviglio, L. (1972). An algebraic alter ego for the classical hierarchy of recognizers. Research report School of Information and Computer Science, Georgia Institute of Technology, Atlanta Georgia. Slamecka, V. and Gehl. J. M. (1972). Requirements for a data base management system. In Ideas for Management: Proc. of the 1972 Int. Systems Meeting, Miami, Florida. Slamecka. V., Zunde. P. and Dexter, M. E. (1970). Data Collection, organization and use. In Proc. of the 1970 Int. Systems Meeting, Las Vegas, Nevada. Tsui, F. (1974). Parallel and Sequential Operations with Array Processors. Ph.D. Thesis. School of Information and Computer Science, Georgia Institute of Technology, Atlanta, Georgia. Winner, R. I. (1975). Toward the primary logics of programming languages. In Proc. of the 1975 Association for Computing Machinery Computer Science Conf., Washington, DC. 4. THEORY
OF SYSTEMS
has been pointed out that the concept of a system is central to almost all areas of information processing and decision making. In general, the notion of a system is introduced to denote the existence of relationships between the data or variables that are observed, or more specifically the existence of a transformation of some set of data into another set. The notion of a system can in a certain sense be considered to be counterpart to the notion of a physical object; just as different physical theories deal with different kinds of physical objects, various aspects of information processing and decision making theories deal with various types of “systems” and their behavior, transformations, control, etc. The theory of information processing and decision making can be considered therefore to be a theory of systems. Of particular interest to this School have been aspects of system theory which are applicable to information system analysis and design. Theoretical research performed in this subject field will be presented under the following headings: theory of dynamical systems; modeling and simulation; and information system design. It
Theory of dynamical systems
Dynamical systems are of great theoretical and practical interest to information scientists. Of course deterministic automata form a subclass of these systems. One of the topics of the School’s research in this area has been the relation between controllability, observability and invariance as