On the number of functions of k-valued logic which are polynomials modulo composite k

Abstract

Abstract A function of k-valued logic is called polynomial if it may be represented by a polynomial modulo k. For any composite number k we propose a uniquely defined canonical form of polynomials for polynomial functions of k-valued logic depending on an arbitrary number of variables. This canonical form is used to find, for any composite k, a formula for the number of n-place polynomial functions of k-valued logic. As a corollary, for any composite k we find the asymptotic behaviour of the logarithm of the number of n-place polynomial functions of k-valued logic.