On the calculation of generalized Reed-Muller canonical expansions from disjoint cube representation of Boolean functions

Abstract

An algorithm that converts disjoint cube representation of Boolean functions into fixed-polarity generalized Reed-Muller expansions (GRME) is presented. Since the known fast algorithm that generates the GRME based on the factorization of the Reed-Muller transform matrix always start from the truth table (minterm) of Boolean function, then the described method has an advantage due to smaller required computer memory. Moreover, for the Boolean functions described by only a few disjoint cubes the method is much more efficient than the fast algorithm. >