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Boolean Functions: Theory, Algorithms, and Applications
Crama, Yves  ; Hammer, Peter L.
2011 • Cambridge University Press, New York, United States - New York
 

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Keywords :
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
Abstract :
[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.
Research center :
QuantOM
Disciplines :
Quantitative methods in economics & management
Mathematics
Computer science
Electrical & electronics engineering
Author, co-author :
Crama, Yves  ;  Université de Liège - ULiège > HEC-Ecole de gestion : > UER Operations - QuantOM
Hammer, Peter L.;  Rutgers University (New Jersey) - RU > RUTCOR
Language :
English
Title :
Boolean Functions: Theory, Algorithms, and Applications
Publication date :
2011
Publisher :
Cambridge University Press, New York, United States - New York
ISBN/EAN :
9780521847513
Number of pages :
xxi, 687
Collection name :
Encyclopedia of Mathematics and its Applications 142
Commentary :
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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