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Boolean Functions
Theory, Algorithms, and Applications

$169.99 (C)

Part of Encyclopedia of Mathematics and its Applications

Peter L. Hammer, Alexander Kogan, Yves Crama, Kazuhisa Makino, Bruno Simeone, Endre Boros, Martin C. Golumbic, Vladimir Gurvich, Lisa Hellerstein, Toshihide Ibaraki, Claude Benzaken, Nadia Brauner
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  • Date Published: May 2011
  • availability: Available
  • format: Hardback
  • isbn: 9780521847513

$169.99 (C)

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About the Authors
  • 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.

    • The breadth and comprehensiveness of coverage reflects special expertise of authors
    • This book emphases algorithms and applications
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    Reviews & endorsements

    "“[T]he unifying role played by Boolean functions [...] and models should probably provide the main motivation for studying this book.” Strike “probably”: this outstanding book will enrich you along several axes."
    George Hacken, Computing Reviews

    "Boolean Functions: Theory, Algorithms, and Applications will undoubtedly become the bible of Boolean functions because it covers this topic in depth and presents the various aspects of these functions in a comprehensive way. Where it stops, research starts.
    The book is written in an extremely didactic style. Many concepts and definitions are introduced progressively and examples are interspersed throughout the text, allowing the reader to easily assimilate more advanced material as it is presented.
    In summary, Boolean Functions: Theory, Algorithms, and Applications shows the extensive experience and deep knowledge the authors and their coauthors have about Boolean functions. It is a reference in which every researcher and user of discrete concepts will find a mine of useful concepts and methods presented in a clear and systematic way."
    Dominique de Werra for Interfaces

    "As a complement to this monograph, readers are advised to refer to the collection of papers [Boolean models and methods in mathematics, computer science, and engineering, Encyclopedia Math. Appl., 134, Cambridge Univ. Press, Cambridge, 2010]. Combined, these two books provide a comprehensive and unified presentation of the theory of Boolean functions incluing its structural algroithmic and applied aspects to a spectacular depth. We are all grateful to the authors for writing such an extensive monograph."
    Sugata Gangopadhyay, Mathematical Reviews

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    Product details

    • Date Published: May 2011
    • format: Hardback
    • isbn: 9780521847513
    • length: 710 pages
    • dimensions: 234 x 156 x 43 mm
    • weight: 1.26kg
    • contains: 98 b/w illus. 227 exercises
    • availability: Available
  • 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 Brauner.

  • Authors

    Yves Crama, Université de Liège, Belgium
    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.

    Peter L. Hammer, Rutgers University, New Jersey
    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.


    Peter L. Hammer, Alexander Kogan, Yves Crama, Kazuhisa Makino, Bruno Simeone, Endre Boros, Martin C. Golumbic, Vladimir Gurvich, Lisa Hellerstein, Toshihide Ibaraki, Claude Benzaken, Nadia Brauner

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