Showing papers on "ω-automaton 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...

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.

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.

Fuzzy-state automata: Their stability and fault tolerance

Abstract: A unified treatment of stable behavior and fault tolerance of finite automata based on the concepts of tolerance spaces and fuzrelations is given. In particular, attractor sets of automata states, approximate fixed points, and almost periodicity of state transitions of finite automata are investigated.

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.

On testing simple hypotheses in finite time with Hellman-Cover automata

Abstract: Asymptotically \varepsilon -optimal automata were developed by Hellman and Cover [4] for testing simple hypotheses concerning the parameter of an independent identically distributed sequence of Bernoulli random variables. These automata permit transitions only between adjacent states and employ artificial randomization only at extreme states. In this paper we study the problem of approximating the optimal Hellman-Cover automaton in fixed-sample-size problems. It is shown that the optimal level of the parameter, which regulates the probability of transitions out of an extreme state, tends to zero at the rate \ln n/n in symmetric testing problems where n is the sample size. We develop an approximation for the optimal parameter value valid for n sufficiently large.

On some elementary properties of uniform automata

Abstract: — Uniform automata are special topological automata, where ail maps are uniformly continuons, lt is shown, that for these automata the existence problem of topological minimal automata and the « topological black box problem » have natural solutions. New uniformitiesfor the state spaces are introduced and their appropriateness for finite approximations is proved.

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 Periodic Equivalents of Finite Automata

Abstract: This correspondence deals with the problem of finding periodic equivalents of finite automata, The idea of periodic equivalent is a generalization of the concept of strictly periodic equivalent studied in [4]. In this correspondence some essential properties of periodic equivalents of finite automata are investigated. Further-more, the concept of strong kernel of automaton is introduced and some connections of strong kernels with periodic equivalents are presented. Finally, the algorithm for determining minimal periodic equivalents of automata is given.

Problems of the Change of Operating Time of Finite Automata

Abstract: The necessary and sufficient condition for the finite automata quasicontrollability defined here is presented. For a given set @ of automata the conditions for the existence of an automaton A such that for each member of @ there exists an identical subautomaton of A, associated with the change of operating time of A, are also given.

On the number of automorphisms of non-cyclic automata

Abstract: Various results are available on the number of automorphisms of an automaton. For the class of cyclic automata the best result is Bavel's [1]: the number of automorphisms divides the number of generators of the automaton. For the class of non-cyclic automata the only result seems to be Feichtinger's [4], who gives an upperbound to the number of automorphisms of a non-cyclic automaton. In this note it will be shown that the number of automorphisms divides Feichtinger's bound, which generalizes Bavel's result to the class of non-cyclic automata.