EMA-FPRMs: An efficient minimization algorithm for fixed polarity Reed-Muller expressions

Fixed polarity Reed-Muller expressions (FPRMs) are well-suited for many practical applications due to they have many excellent properties. In order to obtain an optimal FPRM with fewest product terms, we propose an efficient minimization algorithm (EMA-FPRMs) for FPRMs. The main idea behind the EMA-FPRMs is that, firstly, the incompletely specified Boolean function is transformed into the zero polarity incompletely specified fixed polarity RM expression (ISFPRM) by using the proposed ISFPRM acquisition algorithm; secondly, the polarity and allocation of don't care terms of ISFPRM is encoded as chromosome; lastly, the optimal FPRM with fewest product terms is obtained by using genetic algorithm (GA), in which the FPRM that corresponds to the given chromosome is obtained by using the proposed chromosome conversion algorithm. The experimental results on MCNC benchmark circuits show that compared with the traditional polarity optimization approach which neglects the don't care terms, the EMA-FPRMs is highly effective in minimizing the number of product terms of FPRMs. Moreover, the EMA-FPRMs is faster than the GA based minimization algorithm which also considers the don't care terms.