Reed-Muller tree-based minimisation of fixed polarity Reed-Muller expansions

A heuristic method for the determination of optimum or near-optimum fixed polarity Reed-Muller (FPRM) representation of multiple output, completely specified Boolean systems is presented. The Reed-Muller (RM) tree representation forms the conceptual framework for the method, which involves manipulations of arrays of cubes. A coding method that is well adapted to RM tree representation is presented. The minimisation method takes as input a disjoint sum of cubes representation of the Boolean system. Using Karpovsky´s complexity estimates as the basis for polarity selection, the method obtains the FPRM expansion by generating in one run an optimum or near optimum Reed-Muller tree representation