Showing papers on "Continuous automaton published in 1966"

Testing and generating infinite sequences by a finite automaton

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 of

Generalized decomposition of incomplete finite automata

Abstract: The problem of decomposing a finite automaton has been investigated by many authors [7,8,9,16] However, their results were based on the question of decomposing an automaton into series and parallel connections of automata The present work is an extension to the problem of generalized decomposition where two-way interconnections between automata are permitted Our decomposition does not presuppose the logical design of the circuit of an automaton With the new technology, the problem of economical realization no longer lies in the actual complexity of the logical design in each building block Aside from a given upper limit, the complexity is not reflected in the cost Subject to the restraint of the given limit on each block, the main object is to minimize the number of interconnections between blocks of a generalized decomposition of an automaton