Complexity of Infinite-Domain Constraint Satisfaction

Introduces the universal-algebraic approach to classifying the computational complexity of constraint satisfaction problems.

Manuel Bodirsky (Author)

9781107042841, Cambridge University Press

Hardback, published 10 June 2021

300 pages
23.5 x 15.8 x 3.4 cm, 0.95 kg

'… this book is essential reading for anyone with the vaguest interest in computational complexity, as well as for those curious about potential applications of model theory and universal algebra. It brings together decades of intense research by different research communities in a uniform format.' Victor Lagerkvist, MathSciNet

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.

1. Introduction to constraint satisfaction problems
2. Model theory
3. Primitive positive interpretations
4. Countably categorical structures
5. Examples
6. Universal algebra
7. Equality constraint satisfaction problems
8. Datalog
9. Topology
10. Oligomorphic clones
11. Ramsey theory
12. Temporal constraint satisfaction problems
13. Non-dichotomies
14. Conclusion and outlook
References
Index.

Subject Areas: Artificial intelligence [UYQ], Mathematical theory of computation [UYA], Combinatorics & graph theory [PBV], Mathematical logic [PBCD]