Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions
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S. P. Gorshkov
Abstract
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.
© de Gruyter 2009
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Articles in the same Issue
- Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Hölder metric
- New methods of investigation of perfectly balanced Boolean functions
- On completeness and A-completeness of S-sets of determinate functions containing all one-place determinate S-functions
- On repetition-free Boolean functions over pre-elementary monotone bases
- Maximal groups of invariant transformations of multiaffine, bijunctive, weakly positive, and weakly negative Boolean functions
- Asymptotic normality of the number of absent noncontinuous chains of outcomes of independent trials
- On a class of statistics of polynomial samples
- Score lists in [h-k]-bipartite hypertournaments
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