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

Format:

Book

Author/Creator:

Crama, Yves, 1958- author.

Hammer, P. L., 1936-2006, author.

Series:

Encyclopedia of mathematics and its applications.

Encyclopedia of mathematics and its applications

Language:

English

Subjects (All):

Algebraic functions.

Algebra, Boolean.

Physical Description:

1 online resource (xxi, 687 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2011.

Language Note:

English

Summary:

Written by prominent experts in the field, this monograph provides the first comprehensive, 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. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth 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 for the first time. Because of the depth and breadth 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.

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:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-21829-2

1-283-12720-2

1-139-07459-8

9786613127204

1-139-08139-X

1-139-07684-1

1-139-06880-6

1-139-07912-3

0-511-85200-2

OCLC:

735593475