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Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Mathematics and Applications de Gruyter

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