Complexity of Infinite-Domain Constraint Satisfaction
Manuel Bodirsky
Year: 2021
ISBN: 9781107042841
538 pages. Hardcover.
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Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.
Table of Contents
Acknowledgements
Frontispiece
Chapter 1 – Introduction to constraint satisfaction problems
Chapter 2 – Model Theory
Chapter 3 – Primitive Positive Interpretations
Chapter 4 – Countably Categorical Structures
Chapter 5 – Examples
Chapter 6 – Universal Algebra
Chapter 7 – Equality Constraint Satisfaction Problems
Chapter 8 – Datalog
Chapter 9 – Topology
Chapter 10 – Oligomorphic Clones
Chapter 11 – Ramsey Theory
Chapter 12 – Temporal Constraint Satisfaction Problems
Chapter 13 – Non-Dichotomies
Chapter 14 – Conclusion and Outlook
References
Index