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DOI: 10.4230/LIPIcs.CSL.2024.12

Extending the WMSO+U Logic with Quantification over Tuples

Authors: Anita Badyl and Paweł Parys

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract

We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier 𝖴, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a generalized quantifier 𝖴, expressing the fact that there exist tuples of arbitrarily large finite sets satisfying a given property. First, we prove that the new logic WMSO+𝖴_{tup} is strictly more expressive than WMSO+𝖴. In particular, WMSO+𝖴_{tup} is able to express the so-called simultaneous unboundedness property, for which we prove that it is not expressible in WMSO+𝖴. Second, we prove that it is decidable whether the tree generated by a given higher-order recursion scheme satisfies a given sentence of WMSO+𝖴_{tup}.

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Anita Badyl and Paweł Parys. Extending the WMSO+U Logic with Quantification over Tuples. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{badyl_et_al:LIPIcs.CSL.2024.12,
  author =	{Badyl, Anita and Parys, Pawe{\l}},
  title =	{{Extending the WMSO+U Logic with Quantification over Tuples}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.12},
  URN =		{urn:nbn:de:0030-drops-196557},
  doi =		{10.4230/LIPIcs.CSL.2024.12},
  annote =	{Keywords: Boundedness, logic, decidability, expressivity, recursion schemes}
}

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Extending the WMSO+U Logic with Quantification over Tuples

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