Boolean Functions

Theory, Algorithms, and Applications
Erscheinungsjahr 2014
ISBN: 978-0-521-84751-3
Verlag: Cambridge University Press

Buch, Englisch, 710 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1348 g

Reihe: Encyclopedia of Mathematics and its Applications

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 ist 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.

Autoren/Hrsg.

Crama, Yves

Hammer, Peter L.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

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.

Über Autor(innen)

Crama, Yves
Dr Yves Crama is Professor of Operations Research and Production Management and the former Director General of the HEC Management School of the University of Liège, Belgium. He is widely recognized as a prominent expert in the field of Boolean functions, combinatorial optimization and operations research, and he has coauthored more than 70 papers and three books on these subjects. Dr Crama is a member of the Editorial Board of Discrete Applied Mathematics, Discrete Optimization, the Journal of Scheduling and 4OR - the quarterly journal of the Belgian, French and Italian Operations Research Societies.

Hammer, Peter L.
The late Peter L. Hammer (1936-2006) was a Professor of Operations Research, Mathematics, Computer Science, Management Science and Information Systems at Rutgers University and the Director of Rutgers University Center for Operations Research (RUTCOR). He was the founder and Editor-in-Chief of the journals Annals of Operations Research, Discrete Mathematics, Discrete Applied Mathematics, Discrete Optimization and Electronic Notes in Discrete Mathematics. Dr Hammer was the initiator of numerous pioneering investigations of the use of Boolean functions in operations research and related areas, of the theory of pseudo-Boolean functions, and of the logical analysis of data. He published more than 240 papers and 19 books on these topics.