Functions without short implicents. Part I: lower estimates of weights.

The paper is concerned with n-place Boolean functions not admitting implicents of k variables, 1 ¢ k < n. Estimates for the minimal possible weight w(n, k) of such functions are obtained. It is shown that w(n, 1) = 2, n = 2, 3,…, and w(n, 2) È log2n as n Ù ∞, and moreover, for k > 2 there exists n0 such that w(n, k) > 2k-2 - log2n for all n > n0. [ABSTRACT FROM AUTHOR]