Application of Covering Codes for Reduced Representations of Logic Functions

Abstract

This paper presents a method to derive functional expressions that have an a priory specified number of product terms for various classes of multiple-valued functions. The method exploits the theory of covering codes and it can be tailored for various classes (different sets for values of variables and function values) of multiple-valued functions by selecting appropriately the underlying covering code. The number of product terms in the related functional expression is determined by the covering radius of the code. We present an algorithm to determine the coefficients in these expressions, discuss its complexity, and provide a direct construction to extend the application of this approach to multiple-valued functions for a large number of variables.