Boolean Functions

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

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.