Propagation criterion for monotone Boolean functions with least vector support set of 1 or 2 elements

Abstract

The propagation criterion for monotone Boolean functions with least vector support sets consisting of one or two vectors is studied. We obtain necessary and sufficient conditions for the validity of the propagation criterion for a vector in terms of the Hamming weights of vectors in least vector support set depending on whether these vectors share some nonzero components with the given vector. We find the cardinality of the set of vectors satisfying the propagation criterion for such functions.