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

✍ Scribed by Yves Crama, Peter L. Hammer

• Publisher: Cambridge University Press
• Year: 2010
• Tongue: English
• Leaves: 780
• Series: Encyclopedia of Mathematics and its Applications
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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.