Testing and generating infinite sequences by a finite automaton
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Two apparently divergent areas of inquiry should give rise to the same problem, namely, that of describing the infinite history of finite automata, and it is this problem to which the remainder of this paper will address itself.Abstract:
Bfichi (1962) has given a decision procedure for a system of logic known as \" the Sequential Calculus,\" by showing that each well formed formula of the system is equivalent to a fornmla that, roughly speaking, says something about the infinite input history of a finite automaton. In so doing he managed to answer an open question that was of concern to pure logicians, some of whom had no interest in the theory of automata. Muller (1963) came upon quite similar concepts in studying a problem in asynchronous switching theory. The problem was to describe the behavior of an asynchronous circuit tha t does not reach any stability condition when starting from a certain state and subject to a certain input condition. Many different things can happen, since there is no control over how fast various parts of the circuit react with respect to each other. Since at no time during the presence of that input condition will the circuit reach a terminal condition, it will be possible to describe the total set of possibilities in an ideal fashioll only if an infinite amount of time is assumed for tha t input condition. Neither Biichi's Sequential Calculus nor ~Iuller's problem of asynchronous circuitry will be described further here. I t is interesting tha t two such apparently divergent areas of inquiry should give rise to the same problem, namely, that of describing the infinite history of finite automata. I t is this problem to which the remainder of this paper will address itself. I t will be recalled that a well known basic theorem in the theory ofread more
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References
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Book ChapterDOI
Representation of Events in Nerve Nets and Finite Automata
TL;DR: This memorandum is devoted to an elementary exposition of the problems and of results obtained on the McCulloch-Pitts nerve net during investigations in August 1951.
Proceedings ArticleDOI
Infinite sequences and finite machines
TL;DR: A regular set is a set of possible state sequences of an inputless, nondeterministic machine that may either terminate in some equilibrium condition, or else the machine may pass from one state to another without ever reaching equ~librium.