Simple disjunctive normal forms of Boolean functions with a restricted number of zeros

Abstract

This paper studies the complexity of disjunctive normal forms (DNFs) of Boolean functions defined by their matrices of zeros. The best available bounds are obtained for the minimum number of conjunc� tions making up a DNF of a Boolean function with a restricted number of zeros. The results can be used to implement characteristic functions of classes in pat� tern recognition with binary data [1]. 1. The standard method for constructing DNFs of characteristic classes of functions can be described as follows. Let , , …, and , , …, be given binary descriptions of reference objects of classes K1 and K2, respectively, where , i ∈ {0, 1}, j ∈ {1, 2, …, ki}, is a binary vector of dimension n.