A method for constructing polynomials of k-valued logic functions

Abstract

Functions of &-valued logic are considered. Necessary and sufficient conditions for representability of functions by polynomials modulo k are established for any composite integer k. The canonical form of a polynomial and the way of its construction are given. The complexity of the algorithm for recognizing polynomiality of a function and constructing its polynomial is estimated.

On the closed classes of multivalued logic containing the polynomial class

“…After more than half a century, Kempner [3] proved that any one-place function from P k can be realized by a polynomial modulo k if and only if k is prime. The papers [4][5][6][7][8][9][10][11][12][13] were devoted to the problems of representability of functions from P k by polynomials modulo L Nowadays, interesting results along this line were obtained in [14,15].…”