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CSPs with Few Alien Constraints

Authors Peter Jonsson, Victor Lagerkvist, George Osipov

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LIPIcs.CP.2024.15.pdf
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Subject Classification

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

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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.

Cite As Get 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

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.

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