Issue No. 06 - June (1970 vol. 19)
W.F. Cutlip , Central Washington State College
This paper is based on the following idea. If the two residues x<inf>i</inf>? f(x) and } x?<inf>i</inf>? f(x) are realizable, respectively, with p and q threshold gates, then f is realizable with at most p+q gates. And conversely, if the residues require separately at least r gates, then so does f. Thus, given a table of minimal realizations for 4-argument functions (which require at most three gates), realizations for 5-argument functions can be obtained which are demonstrably minimal or close to it, by considering the five different pairs of residues.
W. Cutlip, "R70-14 Some Results on Cascade Decomposition of Automata," in IEEE Transactions on Computers, vol. 19, no. , pp. 565, 1970.