Abstract
MONOTONIC Boolean functions possessing in some layer a fixed number of unit values are considered. An algorithm for finding the maximum upper zero of such functions is presented. It is compared with an algorithm optimal for the whole set of monotonic functions. It is known that many extremal problems reduce to the problem of searching for the maximum upper zero of a monotonic Boolean function. In [ 11 this problem was solved in the Shannon formulation. Namely, first a monotonic Boolean function of n variables was presented for which it is impossible to solve this problem in less than Ck” “I + 1 steps. Secondly, an algorithm Br is constructed, which for an arbitrary Boolean function of n variables finds its maximum upper zero after not more than CLn”’ + 1 steps. Since in the general case this problem requires lengthy calculations, it appeared of interest to distinguish some subclasses of monotonic Boolean functions for which it can be solved more quickly. In this paper we consider a number of such subclasses and present an algorithm, which on operating with these subclasses guarantees a smaller number of steps than the algorithm B1 described in [ 11. We consider the set Ez n of all binary numbers of length n. We say of two numbers &= (a,, , a,)
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