Document Open Access Logo

CSPs with Few Alien Constraints

Authors Peter Jonsson, Victor Lagerkvist, George Osipov

PDF
Thumbnail PDF

File

LIPIcs.CP.2024.15.pdf
  • Filesize: 0.72 MB
  • 17 pages

Document Identifiers

Author Details

Peter Jonsson
  • Department of Computer and Information Science, Linköping University, Sweden
Victor Lagerkvist
  • Department of Computer and Information Science, Linköping University, Sweden
George Osipov
  • Department of Computer and Information Science, Linköping University, Sweden

Funding

Peter Jonsson and George Osipov: Supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.
  • Jonsson, Peter: Partially supported by the Swedish research council under grant VR-2021-04371.
  • Lagerkvist, Victor: Partially supported by the Swedish research council under grant VR-2022-03214.

Acknowledgements

We thank the anonymous reviewers for helpful suggestions for how to improve the presentation of the paper.

Cite AsGet BibTex

Peter Jonsson, Victor Lagerkvist, and George Osipov. CSPs with Few Alien Constraints. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CP.2024.15

Abstract

The constraint satisfaction problem asks to decide if a set of constraints over a relational structure 𝒜 is satisfiable (CSP(𝒜)). We consider CSP(𝒜 ∪ ℬ) where 𝒜 is a structure and ℬ is an alien structure, and analyse its (parameterized) complexity when at most k alien constraints are allowed. We establish connections and obtain transferable complexity results to several well-studied problems that previously escaped classification attempts. Our novel approach, utilizing logical and algebraic methods, yields an FPT versus pNP dichotomy for arbitrary finite structures and sharper dichotomies for Boolean structures and first-order reducts of (ℕ, =) (equality CSPs), together with many partial results for general ω-categorical structures.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity theory and logic
  • Mathematics of computing → Discrete mathematics
Keywords
  • Constraint satisfaction
  • parameterized complexity
  • hybrid theories

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Libor Barto, Andrei A. Krokhin, and Ross Willard. Polymorphisms, and how to use them. In The Constraint Satisfaction Problem: Complexity and Approximability, volume 7 of Dagstuhl Follow-Ups, pages 1-44. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. Google Scholar
  2. Manuel Bodirsky. Complexity of Infinite-Domain Constraint Satisfaction. Cambridge University Press, 2021. Google Scholar
  3. Manuel Bodirsky and Hubie Chen. Qualitative temporal and spatial reasoning revisited. Journal of Logic and Computation, 19(6):1359-1383, 2009. Google Scholar
  4. Manuel Bodirsky, Hubie Chen, and Michael Pinsker. The reducts of equality up to primitive positive interdefinability. The Journal of Symbolic Logic, 75(4):1249-1292, 2010. URL: https://doi.org/10.2178/jsl/1286198146.
  5. Manuel Bodirsky and Martin Grohe. Non-dichotomies in constraint satisfaction complexity. In Proc. 35th International Colloquium on Automata, Languages and Programming (ICALP-2008), pages 184-196, 2008. Google Scholar
  6. Manuel Bodirsky and Peter Jonsson. A model-theoretic view on qualitative constraint reasoning. Journal of Artificial Intelligence Research, 58:339-385, 2017. Google Scholar
  7. Manuel Bodirsky and Jan Kára. The complexity of equality constraint languages. Theory of Computing Systems, 43(2):136-158, 2008. Google Scholar
  8. Manuel Bodirsky, Jan Kára, and Barnaby Martin. The complexity of surjective homomorphism problems - a survey. Discrete Applied Mathematics, 160(12):1680-1690, 2012. Google Scholar
  9. Manuel Bodirsky and Jaroslav Nešetřil. Constraint satisfaction with countable homogeneous templates. In Proc. 17th International Workshop on Computer Science Logic (CSL-2003), pages 44-57, 2003. Google Scholar
  10. Manuel Bodirsky and Stefan Wölfl. RCC8 is polynomial on networks of bounded treewidth. In Proc. 22nd International Joint Conference on Artificial Intelligence (IJCAI-2011), pages 756-761, 2011. Google Scholar
  11. Elmar Böhler, Edith Hemaspaandra, Steffen Reith, and Heribert Vollmer. Equivalence and isomorphism for Boolean constraint satisfaction. In Proc. 16th International Workshop on Computer Science Logic (CSL-2002), pages 412-426, 2002. Google Scholar
  12. Andrei A. Bulatov. A dichotomy theorem for nonuniform CSPs. In Proc. 58th IEEE Annual Symposium on Foundations of Computer Science (FOCS-2017), pages 319-330, 2017. Google Scholar
  13. Hubie Chen. A rendezvous of logic, complexity, and algebra. ACM SIGACT News, 37(4):85-114, 2006. Google Scholar
  14. David A. Cohen, Peter Jeavons, Peter Jonsson, and Manolis Koubarakis. Building tractable disjunctive constraints. Journal of the ACM, 47(5):826-853, 2000. Google Scholar
  15. Lucien Haddad and Ivo G. Rosenberg. Finite clones containing all permutations. Canadian Journal of Mathematics, 46(5):951-970, 1994. Google Scholar
  16. Peter G. Jeavons. On the algebraic structure of combinatorial problems. Theoretical Computer Science, 200:185-204, 1998. Google Scholar
  17. Sanjiang Li, Zhiguo Long, Weiming Liu, Matt Duckham, and Alan Both. On redundant topological constraints. Artificial Intelligence, 225:51-76, 2015. Google Scholar
  18. Florent R. Madelaine and Barnaby Martin. On the complexity of the model checking problem. SIAM Journal on Computing, 47(3):769-797, 2018. Google Scholar
  19. George Osipov and Magnus Wahlström. Parameterized complexity of equality MinCSP. arXiv preprint arXiv:2305.11131, 2023. This is the report version of a paper that appears in Proc. 31st Annual European Symposium on Algorithms (ESA-2023), pp. 86:1-86:17. Google Scholar
  20. David A. Randell, Zhan Cui, and Anthony G. Cohn. A spatial logic based on regions and connection. In Proc. 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR-1992), pages 165-176, 1992. Google Scholar
  21. Thomas J. Schaefer. The complexity of satisfiability problems. In Proc. 10th Annual ACM Symposium on Theory of Computing (STOC-1978), pages 216-226, 1978. Google Scholar
  22. Henning Schnoor and Ilka Schnoor. Partial polymorphisms and constraint satisfaction problems. In Complexity of Constraints - An Overview of Current Research Themes [Result of a Dagstuhl Seminar], pages 229-254. Springer, 2008. Google Scholar
  23. Moshe Y. Vardi. The complexity of relational query languages (extended abstract). In Proc. 14th Annual ACM Symposium on Theory of Computing (STOC-1982), pages 137-146, 1982. Google Scholar
  24. Dmitriy Zhuk. A proof of the CSP dichotomy conjecture. Journal of the ACM, 67(5):30:1-30:78, 2020. Google Scholar
  25. Dmitriy Zhuk. Constraint satisfaction problem: what makes the problem easy. In Proc. International Conference of Mathematicians 2022 (ICM-2022), pages 1530-1553, 2022. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact