Genetic algorithm for minimization of ESOP representations for multiple-output logic functions

Abstract

This article concerns ESOP representations for multiple-output logic functions. Exclusive-or sum-of-products expression (ESOP) is a formula representing a logic function as an exclusive-or sum of products of variables and their negations. EXOR-based realization leads to reduction in size of logic circuits for many practical logic functions and improves their testability. Minimization of a logic function is a problem of constructing ESOP representation for the given function having the minimal number of summands. We introduce a correspondence between ESOPs for multiple-output logic functions and single-output logic functions and propose genetic algorithm obtaining close to minimal ESOP representations for multiple-output logic functions.