Decomposition of multi-output logic function in Reed-Muller spectral domain

Abstract

The paper deals with the problems of decomposition of set of logic functions in Reed-Muller spectral domain. The approach is based on searching of the common sub-functions for as many as possible logic functions. A decomposition is executed in Reed-Muller spectral domain but Reed-Muller spectrum of multi-output logic function does not exist. Therefore the common sub-functions are searched in the form of the same sub-spectrums in Reed-Muller spectrum of each function. For these functions for which a disjoint Ashenhurst or Curtis decomposition does not exist a non-disjoint decomposition is searched. A specification of non specified states is performed to obtain the same sub-spectrum as exists in spectrum of other functions. The examples show that the approach may be profitable.