Symmetry Groups of Boolean Functions and Constructions of Permutation Groups
نویسندگان
چکیده
منابع مشابه
Symmetry groups of boolean functions
We prove that every abelian permutation group, but known exceptions, is the symmetry group of a boolean function. This solves the problem posed in the book by Clote and Kranakis. In fact, our result is proved for a larger class of groups, namely, for all groups contained in direct sums of regular groups. We investigate the problem of representability of permutation groups by the symmetry groups...
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is called a Boolean function. By Aut(f) we denote the set of all symmetries of f , i.e., these permutation σ ∈ Sn for which f(xσ(1), . . . , xσ(n)) = f(x1, . . . , xn). We show the solution of a problem posed by A. Kisielewicz ([1]). We show that, with the exception of four known groups of small order, every regular permutation group is isomorphic with Aut(f) for some Boolean function f . We pr...
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We study the relations between boolean functions and symmetric groups. We consider elements of a symmetric group as variable transformation operators for boolean functions. Boolean function may be xed or permuted by these operators. We give some properties relating the symmetric group Sn and boolean functions on Vn.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7198