Exact Minimization of Multiple-Valued Functions for PLA Optimization

Abstract

We present an algorithm for determining the minimum representation of an incompletely-specified, multiple-valued input, binary-valued output, function. The overall strategy is similar to the well-known Quine-McCluskey algorithm; however, the techniques used to solve each step are new. The advantages of the algorithm include a fast technique for detecting and eliminating from further consideration the essential prime implicants and the totally redundant prime implicants, and a fast technique for generating a reduced form of the prime implicant table. The minimum cover problem is solved with a branch and bound algorithm using a maximal independent set heuristic to control the selection of a branching variable and the bounding. Using this algorithm, we have derived minimum representations for several mathematical functions whose unsuccessful exact minimization has been previously reported in the literature. The exact algorithm has been used to determine the efficiency and solution quality provided by the heuristic minimize Espresso-MV [11] Also, a detailed comparison with McBoole [2] shows that the algorithm presented here is able to solve a larger percentage of the problems from a set of industrial examples within a fixed allocation of computer resources.