Fast optimization of fixed-polarity Reed-Muller expansions over GF(5) [logic design applications]

An efficient algorithm for optimization of fixed-polarity Reed-Muller (FPRM) expansions over GF(5) is developed in this paper. The new algorithm operates on FPRM expansion in polarity zero of a five-valued function and completely generates its FPRM polarity matrix to obtain its best FPRM expansion. Due to the simplicity and recursive nature of the algorithm, it can be implemented efficiently using fast parallel programming. This, together with low computational cost, enhances the effectiveness of this algorithm, as shown by the presented experimental results. The proposed algorithm can also be utilized to derive FPRM expansions in specific polarities without first constructing the complete polarity matrix.