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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.
R.O. Winder, "R70-13 Multigate Synthesis of General Boolean Functions by Threshold Logic Elements", IEEE Transactions on Computers, vol. 19, no. , pp. 565, June 1970, doi:10.1109/T-C.1970.222984
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