Construction and counting or generalized Boolean functions
نویسندگان
چکیده
منابع مشابه
Counting inequivalent monotone Boolean functions
Monotone Boolean functions (MBFs) are Boolean functions f : {0, 1} → {0, 1} satisfying the monotonicity condition x ≤ y ⇒ f(x) ≤ f(y) for any x, y ∈ {0, 1}. The number of MBFs in n variables is known as the nth Dedekind number. It is a longstanding computational challenge to determine these numbers exactly – these values are only known for n at most 8. Two monotone Boolean functions are inequiv...
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We give a new algorithm counting monotone Boolean functions of n variables (or equivalently the elements of free distributive lattices of n generators). We computed the number of monotone functions of 8 variables which is 56 130 437 228 687 557 907 788. 2001 Elsevier Science B.V. All rights reserved.
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The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over IF2 . Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of in...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90060-x