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Smooth Approximations and Relational Width Collapses

Authors Antoine Mottet , Tomáš Nagy , Michael Pinsker , Michał Wrona

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ACM Subject Classification
  • Theory of computation → Logic
Keywords
  • local consistency
  • bounded width
  • constraint satisfaction problems
  • polymorphisms
  • smooth approximations

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Abstract

We prove that relational structures admitting specific polymorphisms (namely, canonical pseudo-WNU operations of all arities n ≥ 3) have low relational width. This implies a collapse of the bounded width hierarchy for numerous classes of infinite-domain CSPs studied in the literature. Moreover, we obtain a characterization of bounded width for first-order reducts of unary structures and a characterization of MMSNP sentences that are equivalent to a Datalog program, answering a question posed by Bienvenu et al.. In particular, the bounded width hierarchy collapses in those cases as well.

Cite As Get BibTex

Antoine Mottet, Tomáš Nagy, Michael Pinsker, and Michał Wrona. Smooth Approximations and Relational Width Collapses. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 138:1-138:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.138

Author Details

Antoine Mottet
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Tomáš Nagy
  • Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Austria
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Michael Pinsker
  • Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Austria
  • Department of Algebra, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Michał Wrona
  • Theoretical Computer Science Department, Jagiellonian University, Kraków, Poland

Funding

  • Mottet, Antoine: this author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 771005).
  • Nagy, Tomáš: this author has received funding from the Austrian Science Fund (FWF) through project No P32337 and through Lise Meitner Grant No M 2555-N35 and from the Czech Science Foundation (grant No 18-20123S).
  • Pinsker, Michael: this author has received funding from the Austrian Science Fund (FWF) through project No P32337 and from the Czech Science Foundation (grant No 18-20123S).
  • Wrona, Michał: this author is partially supported by National Science Centre, Poland grant number 2020/37/B/ST6/01179.

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