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

doi:10.1017/CBO9780511780448

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.

' … 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 Source: SIGACT News

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
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Introduction
pp ix-xii
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Acknowledgments
pp xiii-xiv
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Contributors
pp xv-xvi
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Acronyms and Abbreviations
pp xvii-xviii
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Boolean Models and Methods in Mathematics, Computer Science, and Engineering
pp xix-xx
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Part I - Algebraic Structures
pp 1-2
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1 - Compositions and Clones of Boolean Functions
pp 3-38
- By Reinhard Pöschel, Technische Universität Dresden, Ivo Rosenberg, Université de Montréal
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2 - Decomposition of Boolean Functions
pp 39-76
- By Jan C. Bioch, Erasmus University Rotterdam
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Part II - Logic
pp 77-78
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3 - Proof Theory
pp 79-98
- By Alasdair Urquhart, University of Toronto
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4 - Probabilistic Analysis of Satisfiability Algorithms
pp 99-159
- By John Franco, University of Cincinnati
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5 - Optimization Methods in Logic
pp 160-194
- By John Hooker, Carnegie Mellon University
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Part III - Learning Theory and Cryptography
pp 195-196
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6 - Probabilistic Learning and Boolean Functions
pp 197-220
- By Martin Anthony, London School of Economics and Political Science
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7 - Learning Boolean Functions with Queries
pp 221-256
- By Robert H. Sloan, University of Illinois at Chicago, Balázs Szörényi, University of Szeged, György Turán, University of Illinois at Chicago
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8 - Boolean Functions for Cryptography and Error-Correcting Codes
pp 257-397
- By Claude Carlet, University of Paris
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9 - Vectorial Boolean Functions for Cryptography
pp 398-470
- By Claude Carlet, University of Paris
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Part IV - Graph Representations and Efficient Computation Models
pp 471-472
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10 - Binary Decision Diagrams
pp 473-505
- By Beate Bollig, Technische Universität Dortmund, Martin Sauerhoff, Technische Universität Dortmund, Detlef Sieling, Technische Universität Dortmund, Ingo Wegener, Technische Universität Dortmund
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11 - Circuit Complexity
pp 506-530
- By Matthias Krause, Mannheim University, Ingo Wegener, Technische Universität Dortmund
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12 - Fourier Transforms and Threshold Circuit Complexity
pp 531-553
- By Jehoshua Bruck, California Institute of Technology
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13 - Neural Networks and Boolean Functions
pp 554-576
- By Martin Anthony, London School of Economics and Political Science
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14 - Decision Lists and Related Classes of Boolean Functions
pp 577-596
- By Martin Anthony, London School of Economics and Political Science
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Part IV - Applications in Engineering
pp 597-598
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15 - Hardware Equivalence and Property Verification
pp 599-674
- By J.-H. Roland Jiang, National Taiwan University, Tiziano Villa, University of Verona
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16 - Synthesis of Multilevel Boolean Networks
pp 675-722
- By Tiziano Villa, University of Verona, Robert K. Brayton, University of California at Berkeley, Alberto L. Sangiovanni-Vincentelli, University of California at Berkeley
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17 - Boolean Aspects of Network Reliability
pp 723-759
- By Charles J. Colbourn, Arizona State University
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