Realizing complex boolean functions with simple groups
نویسندگان
چکیده
منابع مشابه
Most Complex Boolean Functions
It is well known that Exclusive Sum-Of-Products (ESOP) expressions for Boolean functions require on average the smallest number of cubes. Thus, a simple complexity measure for a Boolean function is the number of cubes in its simplest ESOP. It will be shown that this structure-oriented measure of the complexity can be improved by a unique complexity measure which is based on the function. Thus, ...
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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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ژورنال
عنوان ژورنال: Information and Control
سال: 1966
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(66)90229-4