About Some Peculiar Approaches to Seeking the Ashenhurst Decomposition of Logic Functions in the Reed-Muller Spectrum Domain

D. Polok, E. Hrynkiewicz (Silesian Univ. of Techn., Poland)

The paper deals with the problem of logic function decomposition in Reed-Muller spectrum. A logic function decomposition in this domain was interesting because for n variables of a logic function as many as two power n polarizations of Reed-Muller spectrums of the logic function exist and the space where decomposition of such a function can be sought for is extremely large. In the paper there was check if searching for decomposition with spectrum of other polarization then polarization zero leads to a success. Moreover the authors of the paper have observed that it was possible to find a decomposition for some logic functions by making permutations between the functions variables. The paper presents few examples that prove the idea. These findings even more expand the space for seeking for the decomposition.