Use of gray decoding for implementation of symmetric functions

Abstract

We study a problem of reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity Reed-Muller (FPRM) expansions. We propose a method, based on the Gray decoding, for reduction of the number of product terms, and, consequently, the implementation cost of the symmetric functions. The method is founded on the principles of linear transformations of the input variables of an initial function. It provides significant simplification both of the SOPs and the FPRMs representations of the functions. Mathematical analysis as well as experimental results demonstrate the efficiency of the proposed method.