Worst case number of terms in symmetric multiple-valued functions

Abstract

A symmetric multiple-valued function realized as the disjunction of fundamental symmetric functions is addressed. A simpler disjunction can be formed when the latter functions combine in the same way that minterms combine to form simpler product terms for sum-of-products expressions. The authors solve the problem, posed by J.C. Muzio (1990), that sought the worst-case symmetric function in the sense that the maximum number of fundamental symmetric functions is needed. This problem is solved for general radix, and it is shown that the ratio of the maximum size of the disjunction to the total number of fundamental symmetric functions approaches one-half as the number of variables increases.<>