An Iterative Technique for Improved Two-level Logic Minimization

In this paper, we describe an iterative heuristic technique to improve the quality of results obtained during two-level logic minimization using ESPRESSO. Although ESPRESSO minimizes the number of cubes in the solution e#ectively, there are several problem instances where its results are worse than the Quine-McCluskey based exact minimization technique. Our technique is designed to improve the results of ESPRESSO while utilizing ESPRESSO's Unate Recursive Paradigm based optimization heuristics, on account of their simplicity and power. Our technique is based on performing a series of iterations of ESPRESSO, in each of which we extract a number of cubes and append them into a HYPER-COVER. For the given (and subsequent) iterations of ESPRESSO, these cubes are considered as don't care cubes. By e#ectively selecting the number of iterations performed by our heuristic, we can trade o# the improvement in solution quality against the run-time of our algorithm. We have implemented several variants of our iterative algorithm, and have compared their e#ectiveness. We show that with a small number of iterations, our technique is able to improve on the number of cubes in the solution, with an acceptable run-time overhead. The best variant is able to improve the ESPRESSO cube count by up to 18%, with an acceptable increase in run-time. In 58 examples where the ESPRESSO results can be potentially improved, one of the variants of our algorithm demonstrated better results than ESPRESSO for 27 cases