On the Time Necessary to Compute Switching Functions
IEEE Transactions on Computers
B70-5 Theories of Abstract Automata
IEEE Transactions on Computers
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In this paper two closely related problems in automata theory are considered: 1) What is the time required for a network of elements, each with a limited number of inputs, to compute a finite function? 2) What is the time required for a finite automaton, realized as such a network, to compute its output function? Winograd has considered the first problem, especially for addition and group multiplication [1] and numerical multiplication [2]. By laying bare the methodology implicit in his work, we form a basis upon which we can erect a thoroughgoing analysis of multiplication in groups and semigroups and also can analyze computation of various finite functions. This paper presents the beginning of such an analysis.