Fast Minimization of Fixed Polarity Reed-Muller Expressions

Logic minimization has recently attracted significant attention because in many applications it is important to have a compact representation as possible. In this paper, we propose a fast minimization algorithm (FMA) of fixed polarity Reed-Muller expressions (FPRMs). The main idea behind the FMA is to search the minimum FPRM with the fewest products by using the proposed binary differential evolution algorithm (BDE). The BDE can efficiently maintain population diversity and achieve a better tradeoff between the exploration and exploitation capabilities by use of proposed binary random mutation operator and improved selection operator. The experimental results on 24 MCNC benchmark circuits demonstrate that the FMA outperforms the genetic algorithm-based and simulated annealing genetic algorithm-based FPRMs minimization algorithms in terms of accuracy of solutions and solving efficiency. To the best of our knowledge, we are the first to use differential evolution algorithm to minimize FPRMs. The FMA can be extended to derive a minimum mixed polarity Reed-Muller expression.