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Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2020.131
Hrushovski’s Encoding and ω-Categorical CSP Monsters

Authors: Pierre Gillibert, Julius Jonušas, Michael Kompatscher, Antoine Mottet, and Michael Pinsker

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We produce a class of ω-categorical structures with finite signature by applying a model-theoretic construction - a refinement of an encoding due to Hrushosvki - to ω-categorical structures in a possibly infinite signature. We show that the encoded structures retain desirable algebraic properties of the original structures, but that the constraint satisfaction problems (CSPs) associated with these structures can be badly behaved in terms of computational complexity. This method allows us to systematically generate ω-categorical templates whose CSPs are complete for a variety of complexity classes of arbitrarily high complexity, and ω-categorical templates that show that membership in any given complexity class cannot be expressed by a set of identities on the polymorphisms. It moreover enables us to prove that recent results about the relevance of topology on polymorphism clones of ω-categorical structures also apply for CSP templates, i.e., structures in a finite language. Finally, we obtain a concrete algebraic criterion which could constitute a description of the delineation between tractability and NP-hardness in the dichotomy conjecture for first-order reducts of finitely bounded homogeneous structures.
Cite as

Pierre Gillibert, Julius Jonušas, Michael Kompatscher, Antoine Mottet, and Michael Pinsker. Hrushovski’s Encoding and ω-Categorical CSP Monsters. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 131:1-131:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gillibert_et_al:LIPIcs.ICALP.2020.131,
  author =	{Gillibert, Pierre and Jonu\v{s}as, Julius and Kompatscher, Michael and Mottet, Antoine and Pinsker, Michael},
  title =	{{Hrushovski’s Encoding and \omega-Categorical CSP Monsters}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{131:1--131:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.131},
  URN =		{urn:nbn:de:0030-drops-125387},
  doi =		{10.4230/LIPIcs.ICALP.2020.131},
  annote =	{Keywords: Constraint satisfaction problem, complexity, polymorphism, pointwise convergence topology, height 1 identity, \omega-categoricity, orbit growth}
}
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