On the minimization k-valued logic functions in the class of disjunctive normal forms

Abstract

The paper considers the representation of k-valued logical functions in the class of disjunctive normal forms. Various classes of monotone functions of k-valued logic are investigated. Theorems are proved on the coincidence of reduced and shortest disjunctive nominal forms of k-valued functions. For a certain class of k-valued monotone functions, we prove an estimate for the number of functions in this class. we prove criteria for the absorption of elementary conjunctions by a first-order neighborhood of disjunctive normal forms of k-valued functions.