Boolean Models and Methods in Mathematics, Computer Science, and Engineering

Yves Crama (Université de Liège, Belgium), Peter L. Hammer

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English

Cambridge University Press
28 June 2010

Optimisation; Algorithms & data structures

Series: Encyclopedia of Mathematics and its Applications

This collection of papers presents a series of in-depth examinations of a variety of advanced topics related to Boolean functions and expressions. The chapters are written by some of the most prominent experts in their respective fields and cover topics ranging from algebra and propositional logic to learning theory, cryptography, computational complexity, electrical engineering, and reliability theory. Beyond the diversity of the questions raised and investigated in different chapters, a remarkable feature of the collection is the common thread created by the fundamental language, concepts, models, and tools provided by Boolean theory. Many readers will be surprised to discover the countless links between seemingly remote topics discussed in various chapters of the book. This text will help them draw on such connections to further their understanding of their own scientific discipline and to explore new avenues for research.

Edited by: Yves Crama (Université de Liège Belgium), Peter L. Hammer
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 134
Dimensions: Height: 243mm, Width: 163mm, Spine: 47mm
Weight: 1.220kg
ISBN: 9780521847520
ISBN 10: 0521847524
Series: Encyclopedia of Mathematics and its Applications
Pages: 780
Publication Date: 28 June 2010
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

Part I. Algebraic Structures: 1. Compositions and clones of Boolean functions Reinhard Pöschel and Ivo Rosenberg; 2. Decomposition of Boolean functions Jan C. Bioch; Part II. Logic: 3. Proof theory Alasdair Urquhart; 4. Probabilistic analysis of satisfiability algorithms John Franco; 5. Optimization methods in logic John Hooker; Part III. Learning Theory and Cryptography: 6. Probabilistic learning and Boolean functions Martin Anthony; 7. Learning Boolean functions with queries Robert H. Sloan, Balázs Szörényi and György Turán; 8. Boolean functions for cryptography and error-correcting codes Claude Carlet; 9. Vectorial Boolean functions for cryptography Claude Carlet; Part IV. Graph Representations and Efficient Computation Models: 10. Binary decision diagrams Beate Bollig, Martin Sauerhoff, Detlef Sieling and Ingo Wegener; 11. Circuit complexity Matthias Krause and Ingo Wegener; 12. Fourier transforms and threshold circuit complexity Jehoshua Bruck; 13. Neural networks and Boolean functions Martin Anthony; 14. Decision lists and related classes of Boolean functions Martin Anthony; Part V. Applications in Engineering: 15. Hardware equivalence and property verification J. H. Roland Jiang and Tiziano Villa; 16. Synthesis of multi-level Boolean networks Tiziano Villa, Robert K. Brayton and Alberto L. Sangiovanni-Vincentelli; 17. Boolean aspects of network reliability Charles J. Colbourn.

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 on these subjects. Dr Crama is a member of the Editorial Board of Discrete Optimization, 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 the 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 has published more than 240 papers and 19 books on these topics.

Reviews for Boolean Models and Methods in Mathematics, Computer Science, and Engineering

' … is likely to become the reference book for applications of Boolean functions. A common effort of twenty two authors and two editors, leading experts in their fields, the monograph, over 700 pages long, covers all important topics and presents state-of-the-art of applications of Boolean functions. This well written volume can be useful to graduate students, researchers in discrete mathematics, computer science, or other fields, as well as practitioners of operations research and combinatorial optimization. Also readers like me, who want to learn more about Boolean functions, will find this volume very informative.' Marcin Kaminski, SIGACT News