Calculation of sign Walsh spectra of Boolean functions from disjoint cubes

Abstract

Efficient method to generate sign Walsh spectra directly from the reduced representation of Boolean functions in the form of disjoint cubes is proposed. By operating on reduced representation and not the truth vector, the developed method computes the sign Walsh spectra faster with a smaller computer memory and the memory requirements for the storage of sign Walsh spectra are exactly the same as those for original Boolean functions. The algorithm is especially efficient for such Boolean functions that are described by only few disjoint cubes.