Boolean Functions
Boolean Functions
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(C) USDWritten 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.
- The breadth and comprehensiveness of coverage reflects special expertise of authors
- This book emphases algorithms and applications
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
Product details
May 2011Hardback
9780521847513
710 pages
240 × 162 × 51 mm
1.12kg
98 b/w illus. 227 exercises
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.
