Boolean Functions
Theory, Algorithms, and Applications

Provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions.

Yves Crama (Author), Peter L. Hammer (Author)

9780521847513, Cambridge University Press

Hardback, published 16 May 2011

710 pages, 98 b/w illus. 227 exercises
24 x 16.2 x 5.1 cm, 1.12 kg

'Because of the unique depth and breadth of the unified treatment that it provides and its emphasis on algorithms and applications, this monograph and its companion book [Boolean Models and Methods in Mathematics, Computer Science and Engineering] will have special appeal for a large circle of readers.' Sergiu Rudeanu, Zentralblatt MATH

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.

Part I. Foundations: 1. Fundamental concepts and applications
2. Boolean equations
3. Prime implicants and minimal DNFs Peter L. Hammer and Alexander Kogan
4. Duality theory Yves Crama and Kazuhisa Makino
Part II. Special Classes: 5. Quadratic functions Bruno Simeone
6. Horn functions Endre Boros
7. Orthogonal forms and shellability
8. Regular functions
9. Threshold functions
10. Read-once functions Martin C. Golumbic and Vladimir Gurvich
11. Characterizations of special classes by functional equations Lisa Hellerstein
Part III. Generalizations: 12. Partially defined Boolean functions Toshihide Ibaraki
13. Pseudo-Boolean functions
Appendix A. Graphs and hypergraphs
Appendix B. Algorithmic complexity
Appendix C. JBool: a software tool Claude Benzaken and Nadia Brauner.

Subject Areas: Algorithms & data structures [UMB], Optimization [PBU]