On spectra of many-valued logic symmetric functions

Abstract

Many-valued logic symmetric functions appearing in various applications are investigated from the standpoint of determining the number of n-ary functions belonging to a considered set (called the spectrum of the set). Respective spectra are given of k-valued functions that are p-symmetric, self-dual, and self-dual p-symmetric, where p is a partition of {1,...,n}. It is proved that there exist self-dual totally symmetric n-ary k-valued logic functions if and only if the greatest common divisor of k and n is equal to one. A test for detecting the self-dual symmetry property is described. Respective spectra are also given of k-valued symmetric functions that are threshold, multithreshold, monotone, and unate (for the monotone and unate functions k = 3 only).