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Complexity Classifications of Boolean Constraint Satisfaction ProblemsComplexity Classifications of Boolean Constraint Satisfaction Problems

Nadia Creignou, Sanjeev Khanna, and Madhu Sudan



SIAM Monographs on Discrete Mathematics and Applications 7

Many fundamental combinatorial problems, arising in such diverse fields as artificial intelligence, logic, graph theory, and linear algebra, can be formulated as Boolean constraint satisfaction problems (CSP). This book is devoted to the study of the complexity of such problems. The authors' goal is to develop a framework for classifying the complexity of Boolean CSP in a uniform way. In doing so, they bring out common themes underlying many concepts and results in both algorithms and complexity theory. The results and techniques presented here show that Boolean CSP provide an excellent framework for discovering and formally validating "global" inferences about the nature of computation.

This book presents a novel and compact form of a compendium that classifies an infinite number of problems by using a rule-based approach. This enables practitioners to determine whether or not a given problem is known to be computationally intractable. It also provides a complete classification of all problems that arise in restricted versions of central complexity classes such as NP, NPO, NC, PSPACE, and #P.

Audience

This volume will be of interest to both researchers and practitioners working in combinatorial optimization and complexity theory. It is suitable for use as a supplementary text in courses on approximation and computational complexity.

Contents

Preface; Chapter 1: Introduction; Chapter 2: Complexity Classes; Chapter 3: Boolean Constraint Satisfaction Problems; Chapter 4: Characterizations of Constraint Functions; Chapter 5: Implementation of Functions and Reductions; Chapter 6: Classification Theorems for Decision, Counting and Quantified Problems; Chapter 7: Classification Theorems for Optimization Problems; Chapter 8: Input-Restricted Constrained Satisfaction Problems; Chapter 9: The Complexity of the Meta-Problems; Chapter 10: Concluding Remarks; Bibliography; Index

2001 / xii + 106 pages / Hardcover / ISBN-13: 978-0-898714-79-1 / ISBN-10: 0-89871-479-6 /
List Price $75.50 / SIAM Member Price $52.85 / Order Code DT07
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