@MISC{Jukna90monotonecircuits, author = {Stasys Jukna}, title = {Monotone Circuits and Local Computations}, year = {1990} }

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Abstract

here ¯(f) stands for the size of the largest minterm of f and Mn is the set of all monotone Boolean functions on n variables. Definition: A sequence of functions [f n ] = ff 1 ; f 2 ; : : :g is called to be (m; d)-local (with respect to polynomial-size monotone circuits) if there exists a sequence of circuits [Cn ] = fC 1 ; C 2 ; : : :g such that, for each n (i) Cn is over the basis M m;d , (ii) Cn computes f , and (iii) size(Cn ) n O(1) . Theorem 1 (Razborov [1,2]): Let k<F30.84