Boolean Functions: Theory, Algorithms, and Applications

ISBN-13: 9780521847513 / Angielski / Twarda / 2011 / 710 str.

Yves Crama

Opis

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 in this framework 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 unique depth and breadth of the unified treatment that it provides and of 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.

Recenzje

'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

Spis treści

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.