Average case complexity of DNFs and Shannon semi-effect for narrow subclasses of boolean functions

Abstract: In this paper we establish some bounds on the complexity of disjunctive normal forms of boolean function from narrow subclasses (e.g. functions takes value 0 in a limited number of points). The bounds are obtained by reduction the initial problem to a simple set covering problem. The nature of the complexity bounds provided is tightly connected with Shannon effect and semi-effect for this classes.