Some Algorithms for Synthesizing Schemes of Minimal Depth
As is well known, any function of the two-valued algebra of logic (FAL) can be realized in the basis &, V, ˥ by a scheme of depth 2 (if by depth we understand the maximal number of alternations of the operators & and V). Such a scheme is obtained in modeling normal forms of FAL . With this, an asymptotic bound on the complexity of the scheme equals n·2n−1, where n is the number of variables. Lupanov  showed that any FAL is realized in basis &, V, ˥ by a scheme of depth 3 with asymptotic bound on its complexity of 2n/log2n. With a further increase in depth, this bound is not changed.
KeywordsLoad Factor Minimal Depth Disjunctive Normal Form Input Element Elementary Product
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