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Containment for Guarded Monotone Strict NP

Authors Alexey Barsukov , Michael Pinsker , Jakub Rydval

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LIPIcs.ICALP.2025.140.pdf
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ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Computational complexity and cryptography
Keywords
  • guarded
  • monotone
  • SNP
  • forbidden patterns
  • query containment
  • recolouring
  • decidability
  • computational complexity
  • ω-categoricity
  • constraint satisfaction
  • homogeneity
  • amalgamation property
  • Ramsey property
  • canonical function

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Abstract

Guarded Monotone Strict NP (GMSNP) extends Monotone Monadic Strict NP (MMSNP) by guarded existentially quantified predicates of arbitrary arities. We prove that the containment problem for GMSNP is decidable, thereby settling an open question of Bienvenu, ten Cate, Lutz, and Wolter, later restated by Bourhis and Lutz. Our proof also comes with a 2NEXPTIME upper bound on the complexity of the problem, which matches the lower bound for containment of MMSNP due to Bourhis and Lutz. In order to obtain these results, we significantly improve the state of knowledge of the model-theoretic properties of GMSNP. Bodirsky, Knäuer, and Starke previously showed that every GMSNP sentence defines a finite union of CSPs of ω-categorical structures. We show that these structures can be used to obtain a reduction from the containment problem for GMSNP to the much simpler problem of testing the existence of a certain map called recolouring, albeit in a more general setting than GMSNP; a careful analysis of this yields said upper bound. As a secondary contribution, we refine the construction of Bodirsky, Knäuer, and Starke by adding a restricted form of homogeneity to the properties of these structures, making the logic amenable to future complexity classifications for query evaluation using techniques developed for infinite-domain CSPs.

Cite As Get BibTex

Alexey Barsukov, Michael Pinsker, and Jakub Rydval. Containment for Guarded Monotone Strict NP. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 140:1-140:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.140

Author Details

Alexey Barsukov
  • Charles University, Prague, Czech Republic
Michael Pinsker
  • Technische Universität Wien, Austria
Jakub Rydval
  • Technische Universität Wien, Austria

Funding

This research was funded in whole or in part by the Austrian Science Fund (FWF) [P 32337, I 5948]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. This research is also funded by the European Union (ERC, POCOCOP, 101071674). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.

Acknowledgements

The first author is thankful to Florent Madelaine for making him aware of the containment problem for GMSNP.

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