DROPS

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.150

Homogeneity and Homogenizability: Hard Problems for the Logic SNP

Authors: Jakub Rydval

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

The infinite-domain CSP dichotomy conjecture extends the finite-domain CSP dichotomy theorem to reducts of finitely bounded homogeneous structures. Every countable finitely bounded homogeneous structure is uniquely described by a universal first-order sentence up to isomorphism, and every reduct of such a structure by a sentence of the logic SNP. By Fraïssé’s Theorem, testing the existence of a finitely bounded homogeneous structure for a given universal first-order sentence is equivalent to testing the amalgamation property for the class of its finite models. The present paper motivates a complexity-theoretic view on the classification problem for finitely bounded homogeneous structures. We show that this meta-problem is EXPSPACE-hard or PSPACE-hard, depending on whether the input is specified by a universal sentence or a set of forbidden substructures. By relaxing the input to SNP sentences and the question to the existence of a structure with a finitely bounded homogeneous expansion, we obtain a different meta-problem, closely related to the question of homogenizability. We show that this second meta-problem is already undecidable, even if the input SNP sentence comes from the Datalog fragment and uses at most binary relation symbols. As a byproduct of our proof, we also get the undecidability of some other properties for Datalog programs, e.g., whether they can be rewritten in the logic MMSNP, whether they solve some finite-domain CSP, or whether they define a structure with a homogeneous Ramsey expansion in a finite relational signature.

Cite as

Jakub Rydval. Homogeneity and Homogenizability: Hard Problems for the Logic SNP. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 150:1-150:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rydval:LIPIcs.ICALP.2024.150,
  author =	{Rydval, Jakub},
  title =	{{Homogeneity and Homogenizability: Hard Problems for the Logic SNP}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{150:1--150:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.150},
  URN =		{urn:nbn:de:0030-drops-202939},
  doi =		{10.4230/LIPIcs.ICALP.2024.150},
  annote =	{Keywords: constraint satisfaction problems, finitely bounded, homogeneous, amalgamation property, universal, SNP, homogenizable}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.151

Identifying Tractable Quantified Temporal Constraints Within Ord-Horn

Authors: Jakub Rydval, Žaneta Semanišinová, and Michał Wrona

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

The constraint satisfaction problem, parameterized by a relational structure, provides a general framework for expressing computational decision problems. Already the restriction to the class of all finite structures forms an interesting microcosm on its own, but to express decision problems in temporal reasoning one has to take a step beyond the finite-domain realm. An important class of templates used in this context are temporal structures, i.e., structures over ℚ whose relations are first-order definable using the usual countable dense linear order without endpoints. In the standard setting, which allows only existential quantification over input variables, the complexity of finite and temporal constraints has been fully classified. In the quantified setting, i.e., when one also allows universal quantifiers, there is only a handful of partial classification results and many concrete cases of unknown complexity. This paper presents a significant progress towards understanding the complexity of the quantified constraint satisfaction problem for temporal structures. We provide a complexity dichotomy for quantified constraints over the Ord-Horn fragment, which played an important role in understanding the complexity of constraints both over temporal structures and in Allen’s interval algebra. We show that all problems under consideration are in P or coNP-hard. In particular, we determine the complexity of the quantified constraint satisfaction problem for (ℚ;x = y⇒ x ≥ z), hereby settling a question open for more than ten years.

Cite as

Jakub Rydval, Žaneta Semanišinová, and Michał Wrona. Identifying Tractable Quantified Temporal Constraints Within Ord-Horn. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 151:1-151:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rydval_et_al:LIPIcs.ICALP.2024.151,
  author =	{Rydval, Jakub and Semani\v{s}inov\'{a}, \v{Z}aneta and Wrona, Micha{\l}},
  title =	{{Identifying Tractable Quantified Temporal Constraints Within Ord-Horn}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{151:1--151:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.151},
  URN =		{urn:nbn:de:0030-drops-202944},
  doi =		{10.4230/LIPIcs.ICALP.2024.151},
  annote =	{Keywords: constraint satisfaction problems, quantifiers, dichotomy, temporal reasoning, Ord-Horn}
}

Search Results

Documents authored by Rydval, Jakub

Homogeneity and Homogenizability: Hard Problems for the Logic SNP

Abstract

Cite as

Identifying Tractable Quantified Temporal Constraints Within Ord-Horn

Abstract

Cite as

Thanks for your feedback!

Could not send message