On the length of functions of κ-valued logic in the class of polynomial normal forms modulo κ

Abstract

AbstractPolynomial normal forms for functions of κ-valued logics (for prime values of κ) are considered. A polynomial normal form modulo κ (p.n.f.) is the sum modulo κ of products of variables, or variables with one or several Post negations, taken with some coefficients. The length of a p.n.f. is the number of distinct terms that appear in the form with nonzero coefficients. If κ is a prime number, then each function of κ-valued logic may be represented by various p.n.f. The length of a function of κ-valued logic in the class of p.n.f. is the minimum length of a p.n.f. representing this function. The Shannon function L