Showing papers on "Automata theory published in 1975"

The logic of automata

Abstract: Automata are the prime example of general systems over discrete spaces, and yet the theory of automata is fragmentary and it is not clear what makes a general structure an automaton. This paper investigates the logical foundations of automata relating it to the semantics of our notions of uncertainty, state and state-determined. A single framework is established for the conventional spectrum of automata: deterministic, probabilistic, fuzzy, and non-deterministic, which shows this set to be, in some sense, complete. Counter-examples are then developed to show that this spectrum alone is inadequate to describe the behaviour of certain forms of uncertain system. Finally a general formulation is developed based on the fundamental semantics of our notion of a state that shows that the logical Structure of an automaton must be at least a positive ordered semiring. The role of probability logic, its relationship to fuzzy logic, the rotes of topological models of automata, and the symmetry between inputs and outp...

From automata theory to brain theory

Abstract: Although the brain modeler can gain many useful insights from such concepts of orthodox automata theory as finite automata, network complexity theory, and Turing machines, we here stress that the best neural modelling will bear little resemblance to a straight application of such techniques. This general perspective is complemented by a survey of eight levels of neural modelling, coupled with an extensive bibliography. The eight levels are: formfunction relations in single neurons; lateral inhibition; mode selection; statistical mechanics; adaptive neural networks; holography; control theory; and cognitive modelling.

On 3-head versus 2-head finite automata

Abstract: A direct proof is given that shows that (one-way) 3-head deterministic finite automata are computationally more powerful than 2-head finite automata.

Logic, biology and automata-some historical reflections

Abstract: This is a historical and philosophical survey of the relation of logic (including automata theory and inductive logic) to the biological sciences, broadly conceived. Aristotle and his successors formalized portions of deductive discourse, but Leibniz was the first to suggest formalizing language as a whole. Since then many different formal languages have been constructed; they are fair models of certain aspects of language. Leibniz saw the computational possibilities of a formal language, which were later made explicit by Turing (1936–37) and Post (1936). In the 1880s Peirce suggested that Boolean algebra could be used to design relay computers and that evolutionary processes and inductive processes are analogous. The first well-developed applications of logic to biology were McCulloch & Pitts's (1943) idealized neuron networks and von Neumann's self-reproducing automata. While these are interesting models, their fit to actual biological phenomena is rough. How may the fit of logic to biology be made closer? Various ways are suggested: more detailed applications, the development of biology in the direction of automata theory, and by using formalisms that combine deduction with induction. Evolution is a statistical or inductive process, but genetic strings play a deductive role. Formal languages are different from natural languages in rigor and precision, yet they give fair models of deduction, induction, and grammar. Other uses of language, such as the empirical, seem basically informal. Consider, however, a computer with appropriate input and output devices which interacts with its environment and communicates in a sophisticated language. It would understand empirical concepts and would verify empirical statements, and hence would model the empirical use of language. The logical design and initial state of any computer, and a fortiori of this computer, can be expressed as a recursive formula of a formal language. Hence the empirical aspect of language is also formalizable.

Approximate identification of automata

Abstract: A technique is described for the identification of probabilistic and other nondeterministic automata from sequences of their input/output behaviour. For a given number of states the models obtained are optimal in well defined senses, one related to least-mean-square approximation and the other to Shannon entropy. Practical and theoretical investigations of the technique are outlined.

Behaviorism, finite automata, and stimulus response theory

Abstract: In this paper it is argued that certain stimulus-response learning models which are adequate to represent finite automata (acceptors) are not adequate to represent noninitial state input-output automata (transducers). This circumstance suggests the question whether or not the behavior of animals if satisfactorily modelled by automata is predictive. It is argued in partial answer that there are automata which can be explained in the sense that their transition and output functions can be described (roughly, Hempel-type covering law explanation) while their behaviors are in principle not predictable short of possession of their complete histories or of information concerning present internal states by indirect observation.

Recognition of fuzzy languages

Abstract: In this paper, we propose the concept of recognition of fuzzy languages by machines such as Turing machines, linear bounded automata, pushdown automata and finite automata. It is shown that it is a reasonable extension of the ordinary concept of recognition of languages by machines. Basic results are given about the recognition theory of fuzzy languages.

Modification tolerance of fuzzy-state automata

Abstract: A treatment of modifiable, finite automata based on the concepts of tolerance spaces and fuzrelations is given. The performance of a modification of an automaton is compared with that of its reference automaton by means of a suitable comparison relation. Relations between modifiable, time-variant, and learning automata are outlined, and the modification masking capacity of certain automata with given tolerance is investigated.

Description of restricted automata by first-order formulae

Abstract: The emptiness problem for stack automata is shown decidable by reducing that problem to a solvable decision problem for the predicate calculus. Similar decision procedures are outlined for classes of weaker automata.

Functional synthesis of systems

Abstract: 1) For the solution of problems of composition and decomposition of nonelementary automata we use a general method which is based on the solution of a system of functional equations. 2) When setting up the system of functional equations we do not impose constraints on the method and level of description of the language of systems. 3) When synthesizing the automata A0, Ai, Bi, the structure of the automaton Ai is not subject to any variation. This is a factor of considerable importance, since here it is possible to have a definite set of automata Ai which enable us to synthesize automata A0 which realize specified functions. 4) The method proposed for the solution of a system of functional equations is applicable for automatization of the design of computer systems.

Automata theory: what is it used for?

Abstract: At the graduate level, it seems like one should not have to be able t o explain theoretical relevance of material in a proof oriented fashion. I f everyone waited for such proof before pursing such material I am afrai d that we all would have rather limited educations. Both the student an d the school must work to bridge the theoretical relevance gap. The schoo l should continually be reviewing its course offerings to assure that th e theory they offer is not too far removed from the more relevant material a s to obscure its benefit. On the other hand, students should know beforehan d the broad scope of each course they take which has a theoretical bent t o assure themselves that they are getting material in which they are interested and which fits their educational plans. What quite often happens i s that a student will take a course and yet have no idea of its content, use , or place in his program. This subject is more than interesting, it is vitally important. It woul d like to know what others have to say. If you have any comments on what I have written, I would be glad to cover them further with you. Probably the question most often asked by graduate student s taking their first Automata Theory (A .T .) course is \"How i s this knowledge used?\". First let me address the question and the n evolve an answer. Such a question is probably the reflectio n of a student, such as an engineer, who is quite interested i n being able to directly apply all that he learns. This contrast s immediately in his first couple of lectures in A .T. becaus e A .T. is very much organized around abstract algebraic concepts. This is not to say that the concepts did not originate in th e real world or that there are not real applications ; quite th e contrary. But because of the representation of concepts in th e abstract, it is quite natural and reasonable for one to ask th e question. And as one progresses further into a first or secon d course in A .T ., this question grows in importance as the studen t finds himself putting in generous amounts of time and effort o n material which is increasingly more abstract. No wonder h …

On the characterization of certain classes of developmental languages by automata

Abstract: A new family of automata, called orderless contraction automata of complexity (0, ∞), is introduced, and it is proved that this family of automata accepts precisely the class of propagating, normal, limited, extended, tabled 0-Lindenmayer languages (Rosenberg [4], Herman [2]). Furthermore a subfamily of this new family of automata accepts precisely the class of propagating, normal, limited, extended 0-Lindenmayer languages.