Edinburgh Napier University

  We present two algorithms in this paper: the first is used to convert between Product of Sums (POS) and Positive Polarity Dual Reed-Muller (PPDRM) forms; while the second algorithm generates all the polarity sets from any polarity set for a single output function. In the optimization of FPDRM expansions, functions with different polarities are usually calculated dierctly from POS expressions. Two FPDRM expansions that have the same number of variables and whose polarities are dual can be derived from each other without starting from POS expressions. Hence, by repeating certain operations on the DRM expansions, all polarities can be derived. This technique finds the best polarity of FPDRM amomg the 2" fixed polarities.The algorithm is based on the dual proprty and the Gray code strategy. Time efficiency and computing speed are achieved in this technique because the information in finding FPDRM expansion of one polarity is utilised by others. The proposed methods are efficient in terms of memory size and CPU time as shown in the experimental results.