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On the classification of Boolean functions
IRE Transactions on Information Theory, 1959Two Boolean functions which differ only by permutation and complementation of their n input variables belong to the same symmetry class. Methods are described for determining the number of symmetry classes for functions of n variables, and for ascertaining whether or not two functions belong to the same class.
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Minimization of Boolean Functions
IEEE Transactions on Computers, 1971The Quine–McCluskey method of minimizing a Boolean function gives all the prime implicants, from which the essential terms are selected by one or more cover tables known as the prime implicant tables. This note describes a tabular method where the essential prime implicants are selected during the process of forming the combination tables, and other ...
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IEEE Transactions on Information Theory, 2012
We show that any Boolean function, in even dimension, equal to the sum of a Boolean function g which is constant on each element of a spread and of a Boolean function h whose restrictions to these elements are all linear, is semibent if and only if g and h are both bent.
Claude Carlet, Sihem Mesnager
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We show that any Boolean function, in even dimension, equal to the sum of a Boolean function g which is constant on each element of a spread and of a Boolean function h whose restrictions to these elements are all linear, is semibent if and only if g and h are both bent.
Claude Carlet, Sihem Mesnager
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Boolean Functions as Models for Quantified Boolean Formulas
Journal of Automated Reasoning, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hans Kleine Büning +2 more
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IEEE Transactions on Electronic Computers, 1964
This paper describes a group theoretic approach to count the number of equivalence classes of invertible Boolean functions under the group operation of complementation, permutation, combinations of complementation and permutation, and linear and affine transformations.
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This paper describes a group theoretic approach to count the number of equivalence classes of invertible Boolean functions under the group operation of complementation, permutation, combinations of complementation and permutation, and linear and affine transformations.
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Approximation of a partial boolean function by a monotonic boolean function
USSR Computational Mathematics and Mathematical Physics, 1978Abstract THE PROBLEM of finding a monotonic Boolean function best approximation a specified partial (not defined everywhere) Boolean function, is solved by a flow algorithm. Among the monotonic functions giving the best approximation, the function possessing the simplest disjunctive normal form is chosen.
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Systems and Computers in Japan, 1991
AbstractAlthough various formal models of learning have been studied in the past, a realistic model taking into consideration the time required for learning has not been proposed. Recently, Valiant [8] proposed a general learning model based on the theory of computational complexity, gave a definition of learnability, and obtained various classes of ...
Qian-Ping Gu, Akira Maruoka
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AbstractAlthough various formal models of learning have been studied in the past, a realistic model taking into consideration the time required for learning has not been proposed. Recently, Valiant [8] proposed a general learning model based on the theory of computational complexity, gave a definition of learnability, and obtained various classes of ...
Qian-Ping Gu, Akira Maruoka
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SUPER-BOOLEAN FUNCTIONS AND FREE BOOLEAN QUASILATTICES
Discrete Mathematics, Algorithms and Applications, 2014A Boolean quasilattice is an algebra with hyperidentities of the variety of Boolean algebras. In this paper, we give a functional representation of the free n-generated Boolean quasilattice with two binary, one unary and two nullary operations. Namely, we define the concept of super-Boolean function and prove that the free Boolean quasilattice with two
Yu. M. Movsisyan, V. A. Aslanyan
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Russian Mathematical Surveys, 2003
Summary: Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published.
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Summary: Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published.
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On the independence of Boolean functions
International Journal of Computer Mathematics, 2005Boolean functions are widely used because they can be used to precisely describe logical circuits. Properties of Boolean functions with respect to their applications to cryptography have been studied, but relationship between Boolean functions are rarely studied.
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