Reference : Boolean Functions: Theory, Algorithms, and Applications
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Physical, chemical, mathematical & earth Sciences : Mathematics
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Boolean Functions: Theory, Algorithms, and Applications
Crama, Yves mailto [Université de Liège - ULiège > HEC-Ecole de gestion : > UER Operations - QuantOM > >]
Hammer, Peter L. [Rutgers University (New Jersey) - RU > RUTCOR > > >]
Cambridge University Press
Encyclopedia of Mathematics and its Applications 142
xxi, 687
New York
[en] Boolean functions ; propositional logic ; satisfiability ; graph theory ; electrical engineering ; reliability ; simple games ; computational complexity ; circuits ; pseudo-Boolean functions ; artificial intelligence ; duality ; integer programming ; combinatorial optimization
[en] This monograph provides the first comprehensive presentation of the theoretical, algorithmic and applied aspects of Boolean functions, i.e., {0,1}-valued functions of a finite number of {0,1}-valued variables.

The book focuses on algebraic representations of Boolean functions, especially normal form representations. It presents the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated representations, dualization, etc.), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once, etc.), and two fruitful generalizations of the concept of Boolean functions (partially defined and pseudo-Boolean functions). It features a rich bibliography of about one thousand items.

Prominent among the disciplines in which Boolean methods play a significant role are propositional logic, combinatorics, graph and hypergraph theory, complexity theory, integer programming, combinatorial optimization, game theory, reliability theory, electrical and computer engineering, artificial intelligence, etc. The book contains applications of Boolean functions in all these areas.
Researchers ; Students
The monograph contains several chapters contributed by prominent experts: Claude Benzaken, Endre Boros, Nadia Brauner, Martin C. Golumbic, Vladimir Gurvich, Lisa Hellerstein, Toshihide Ibaraki, Alexander Kogan, Kazuhisa Makino, and Bruno Simeone.

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JBoolMay2011.zipJBool: A software tool330.98 kBView/Open

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