Boolean Functions: Theory, Algorithms, and Applications

Written by prominent experts in the field, this monograph provides the first comprehensive and unified presentation of the structural, algorithmic, and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. It presents in this framework the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations), and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the unique depth and breadth of the unified treatment that it provides and of its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering, and economics.

Table of Contents

Part I: Foundations
Chapter 1 Fundamental concepts and applications
Chapter 2 Boolean equations
Chapter 3 Prime implicants and minimal DNFs
Chapter 4 Duality theory

Part II: Special Classes
Chapter 5 Quadratic functions
Chapter 6 Horn functions
Chapter 7 Orthogonal forms and shellability
Chapter 8 Regular functions
Chapter 9 Threshold functions
Chapter 10 Read-once functions
Chapter 11 Characterizations by functional equations

Part III: Generalizations
Chapter 12 Partially defined Boolean functions
Chapter 13 Pseudo-Boolean functions

Appendix A: Graphs and hypergraphs
Appendix B: Algorithmic complexity
Appendix C: JBool: A software tool