Abstract
This paper is based on the following idea. If the two residues x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> ⋅ f(x) and } x̄ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">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.
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