Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions
Сергей Павлович Горшков, Alexey Vyacheslavovich Tarasov · Discrete Mathematics and Applications · 2009
We investigate some properties of multiaffine, bijunctive, weakly positive and weakly negative Boolean functions. The following results are proved: for any integer k ≥ 1 the maximal group of transformations of the domain of definition of a function of k variables with respect to which the set of multiaffine Boolean functions is invariant is the complete affine group AGL ( k , 2); for the bijunctive functions of k ≥ 3 variables it is the group of transformations each of which is a combination of a permutation and an inversion of the variables of the function; and for a weakly positive (weakly negative) function of k ≥ 2 variables it is the group of transformations each of which is a permutation of the variables of the function.