Some Observations Related to Searching for Logic Functions Decomposition in Reed-Muller Spectral Domain

The paper deals with the problems of searching for decomposition of Boolean functions in the domain of Reed-Muller spectrum. The Ashenhurst decomposition is considered in the first turn but the decomposition based on Curtis decomposition model was mentioned, too. The special attention was paid for analyzing some problems associated with searching for decomposition with use of spectra with various polarities and to the method of finding beneficial input variables with possible permutations between them. It turned out that searching for decomposition in different polarizations of the Reed-Muller spectral domain was fruitless. But in some cases successful results were achieved owing to permutations between input variables before the Reed-Muller spectrum is calculated. Some promising observations related to that field are also included into this paper.