This research applies a new heuristic combined with a genetic algorithm (GA) to the task of logic minimization for incompletely specified data, with both single and multi-outputs, using the Generalized Reed-Muller (GRM) equation form. The GRM equation type is a canonical expression of the Exclusive-Or Sum-of-Products (ESOPs) type, in which for every subset of input variables there exists not more than one term with arbitrary polarities of all variables. This AND-EXOR implementation has been shown to be economical, generally requiring fewer gates and connections than that of AND-OR logic. GRM logic is also highly testable, making it desirable for FPGA designs. The minimization results of this new algorithm tested on a number of binary benchmarks are given. This minimization algorithm utilizes a GA with a two-level fitness calculation, which combines human-designed heuristics with the evolutionary process, employing Baldwinian learning. In this algorithm, first a pure GA creates certain constraints for the selection of chromosomes, creating only genotypes (polarity vectors), The phenotypes (GRMs) are then learned in the environment and contribute to the GA fitness (which is the total number of terms of the best GRM for each output), providing indirect feedback as to the quality of the genotypes (polarity vectors) but the genotype chromosomes (polarity vectors) remain unchanged. In this process, the improvement in genotype chromosomes (polarity vectors) is the product of the evolutionary processes from the GA only. The environmental learning is achieved using a human-designed GRM minimization heuristic. As much previous research has presented the merit of AND-EXOR logic for its high density and testability, this research is the first application of the GRM (a canonical AND-EXOR form) to the minimization of incompletely specified data. (C) 2001 Published by Elsevier Science B.V.
