Boolean Models and Methods in Mathematics, Computer Science, and Engineering (Encyclopedia of Mathematics and its Applications, Series Number 134)

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-- 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-- Algebraic Structures. Compositions And Clones Of Boolean Functions / Reinhard Pöschel And Ivo Rosenberg -- Decomposition Of Boolean Functions / Jan C. Bioch -- Logic. Proof Theory / Alasdair Urquhart -- Probabilistic Analysis Of Satisfiability Algorithms / John Franco -- Optimization Methods In Logic / John Hooker -- Learning Theory And Cryptography. Probabilistic Learning And Boolean Functions / Martin Anthony -- Learning Boolean Functions With Queries / Robert H. Sloan, Balázs Szörényi, And György Turán -- Boolean Functions For Cryptography And Error-correcting Codes / Claude Carlet -- Vectorial Boolean Functions For Cryptography / Claude Carlet -- Graph Representations And Efficient Computation Models. Binary Decision Diagrams / Beate Bollig ... [et Al.] -- Circuit Complexity / Matthias Krause And Ingo Wegener -- Fourier Transforms And Threshold Circuit Complexity / Jehoshua Bruck -- Neural Networks And Boolean Functions / Martin Anthony -- Decision Lists And Related Classes Of Boolean Functions / Martin Anthony -- Applications In Engineering. Hardware Equivalence And Property Verification / J.-h. Roland Jiang And Tiziano Villa -- Synthesis Of Multi-level Boolean Networks / Tiziano Villa ... [et Al.] -- Boolean Aspects Of Network Reliability / Charles J. Colbourn. Edited By Yves Crama, Peter L. Hammer. Series Numbering From Jacket. Includes Bibliographical References. Contents Preface Introduction Acknowledgements Contributors Acronyms and Abbreviations Part I. Algebraic Structures 1. Compositions and clones of Boolean functions 2. Decomposition of Boolean functions Part II. Logic 3. Proof theory 4. Probabilistic analysis of satisfiability algorithms 5. Optimization methods in logic Part III. Learning Theory and Cryptography 6. Probabilistic learning and Boolean functions 7. Learning Boolean functions with queries 8. Boolean functions for cryptography and error-correcting codes 9. Vectorial Boolean functions for cryptography Part IV. Graph Representations and Efficient Computation Models 10. Binary decision diagrams 11. Circuit complexity 12. Fourier transforms and threshold circuit complexity 13. Neural networks and Boolean functions 14. Decision lists and related classes of Boolean functions Part V. Applications in Engineering 15. Hardware equivalence and property verification 16. Synthesis of multi-level Boolean networks 17. Boolean aspects of network reliability