Multiple-valued Boolean minimization based on graph coloring

Abstract

A method for the minimization of multiple-valued input Boolean functions is presented. It is based on the reduction of logic minimization problem to graph coloring, applied to the graph of incompatibility of implicants. In this approach, two NP-complete problems encountered in the minimization of Boolean functions, i.e. the generation of prime implicants and the covering problem, are reduced to a single, and better understood, graph coloring problem. A special type of implicants, called minimally split product implicants, is generated from an arbitrary set of input cubes that allow optimum results to be obtained. An important result of this method is that it is analytical, rather than heuristic, and gives more insight into a larger class of logic synthesis problems, such as input encoding and Boolean decomposition. >