Representation of incompletely specified binary and multiple-valued logic functions by compact decision diagrams

Abstract

Incompletely specified logic functions are often met in computer science and engineering and their compact representations are a subject of a wide research interest. In this paper, we present a method for determining an assignment of unspecified function values that will produce compact decision diagrams. The method is based on the analysis of Walsh and Vilenkin-Chrestenson spectral coefficients for binary and multiple-valued functions, respectively, and the operation of spectral translation of logic functions. Spectral transforms are used to identify the linear function with strongest correlation with the initial function and assign the unspecified values as well as to specify the spectral translation that will result in a compact decision diagram.