Boolean functions : theory, algorithms, and applications / Yves Crama, Peter L. Hammer.

Format:

Book

Author/Creator:

Crama, Yves, 1958-

Contributor:

Hammer, P. L., 1936-2006.

Series:

Encyclopedia of mathematics and its applications ; v. 142.

Encyclopedia of mathematics and its applications ; 142

Language:

English

Subjects (All):

Algebraic functions.

Algebra, Boolean.

Physical Description:

xxi, 687 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2011.

Contents:

Fundamental concepts and applications

Boolean equations

Prime implicants and minimal DNFs / Peter L. Hammer and Alexander Kogan

Duality theory / Yves Crama and Kazuhisa Makino

Quadratic functions / Bruno Simeone

Horn functions / Endre Boros

Orthogonal forms and shellability

Regular functions

Threshold functions

Red-once functions / Martin C. Golumbic and Vladimir Gurvich

Characterizations of special classes by functional equations / Lisa Hellerstein

Partially defined Boolean functions / Toshihide Ibaraki

Pseudo-Boolean functions

Graphs and hypergraphs

Algorithmic complexity

JBool : a software tool / Claude Benzaken and Nadia Brauner.

Notes:

Includes bibliographical references and index.

"Written by prominent experts in the field, this monograph provides the first comprehensive and unified presentation of the structural, algorithmic, and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. It presents with in this framework the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an indepth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations), and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form forthe first time. Because of the unique depth and breadth of the unified treatment that it provides and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering, and economics"-- Provided by publisher.

ISBN:

0521847516

9780521847513

OCLC:

711777210

Online:

Cover image