Seeking for decomposition of a Boolean function in the reed-müller spectral domain by Means of permutation between function variables

The paper deals with the problem of logic function decomposition in Reed-Muller spectrum. A Boolean function decomposition in this domain is interesting because for n variables of a Boolean function as many as two power n Reed-Muller expansions of the Boolean function exist and the space where decomposition of such a function can be sought for is extremely large. The authors of the paper have observed that it was possible to find a decomposition for some Boolean functions by making permutations between the functions variables. The paper presents few examples that prove the idea. These findings expand the space for seeking for the optimum decomposition even more.