Optimal output assignment and the maximum number of implicants needed to cover the multiple-valued logic functions

Abstract

Optimal output assignment is proposed to reduce the number of implicants in a minimal sum-of-products expression, where sum refers to TSUM. Some bounds on the maximum number of implicants needed to cover an output permuted function are clarified. One-variable output permuted functions require at most p-1 implicants in their minimal sum-of-products expressions, where p is the radix. Two-variable functions with radix between three and six are analyzed. Some speculations on the minimum number of the implicants are confirmed for functions with a higher radix and more than two variables. Computer simulation shows that output-permuted functions require 15% fewer implicants on the average.<>