8th Annual Symposium on Switching and Automata Theory (SWAT 1967) (1967)
Oct. 18, 1967 to Oct. 20, 1967
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.1967.9
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  and numerical multiplication . 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.
M. A. Arbib and P. M. Spira, "Computation times for finite groups, semigroups and automata," 8th Annual Symposium on Switching and Automata Theory (SWAT 1967)(FOCS), Texas, 1967, pp. 291-295.