Generalised k-variable-mixed-polarity Reed-Muller expansions for system of Boolean functions and their minimisation

A lookup table based method to minimise generalised partially-mixed-polarity Reed-Muller (GPMPRM) expansions with k mixed polarity variables is presented. The developed algorithm can produce solutions based on the desired cost criteria for the systems of completely specified functions. A heuristic approach based on the exclusion rule is adopted to extract the best dual polarity variables from any fixed polarity Reed-Muller (FPRM) expansion. The obtained experimental results compared favourably with the recently published results and outperform those generated by the exact minimal FPRM expansion minimisers