Boolean Functions

Boolean Functions : Theory, Algorithms, and Applications

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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 more

Product details

  • Electronic book text | 142 pages
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 98 b/w illus. 227 exercises
  • 113906424X
  • 9781139064248

Table of contents

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 more

Review quote

'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 MATHshow more

About Yves Crama

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 Liege, 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. 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 more

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