An Order out of Nowhere: A New Algorithm for Infinite-Domain {CSP}s

Authors Antoine Mottet , Tomáš Nagy , Michael Pinsker



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Antoine Mottet
  • Research Group on Theoretical Computer Science, Hamburg University of Technology, Germany
Tomáš Nagy
  • Theoretical Computer Science Department, Jagiellonian University, Kraków, Poland
Michael Pinsker
  • Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Austria

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Antoine Mottet, Tomáš Nagy, and Michael Pinsker. An Order out of Nowhere: A New Algorithm for Infinite-Domain {CSP}s. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 148:1-148:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.148

Abstract

We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the classical complexity reduction to finite-domain CSPs that was used in the proof of the complexity dichotomy for such problems cannot be used as a black box in our case. We therefore introduce an algorithmic technique inspired by classical notions from the theory of finite-domain CSPs, and prove its correctness based on symmetries that depend on a linear order that is external to the structures under consideration. Our second main result is a P/NP-complete complexity dichotomy for such problems over many sets of uniform hypergraphs. The proof is based on the translation of the problem into the framework of constraint satisfaction problems (CSPs) over infinite uniform hypergraphs. Our result confirms in particular the Bodirsky-Pinsker conjecture for CSPs of first-order reducts of some homogeneous hypergraphs. This forms a vast generalization of previous work by Bodirsky-Pinsker (STOC'11) and Bodirsky-Martin-Pinsker-Pongrácz (ICALP'16) on graph satisfiability.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
Keywords
  • Constraint Satisfaction Problems
  • Hypergraphs
  • Polymorphisms

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