The Maximal Closed Classes of Unary Functions in p ‐Valued Logic

Source abstract

Abstract In many‐valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many‐valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many‐valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k ‐degree symmetric group S k , which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p ‐valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35.