License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2016.13
URN: urn:nbn:de:0030-drops-65537
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6553/
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Kotek, Tomer ; Veith, Helmut ; Zuleger, Florian

Monadic Second Order Finite Satisfiability and Unbounded Tree-Width

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LIPIcs-CSL-2016-13.pdf (0.6 MB)

Abstract

The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese. We prove that the following problem is decidable:

Input: (i) A monadic second order logic sentence alpha, and (ii) a sentence beta in the two-variable fragment of first order logic extended with counting quantifiers. The vocabularies of alpha and beta may intersect.

Output: Is there a finite structure which satisfies alpha and beta such that the restriction of the structure to the vocabulary of alpha has bounded tree-width? (The tree-width of the desired structure is not bounded.)

As a consequence, we prove the decidability of the satisfiability problem by a finite structure of bounded tree-width of a logic MS^{exists card} extending monadic second order logic with linear cardinality constraints of the form |X_{1}|+...+|X_{r}| < |Y_{1}|+...+|Y_{s}| on the variables X_i, Y_j of the outer-most quantifier block. We prove the decidability of a similar extension of WS1S.

BibTeX - Entry

@InProceedings{kotek_et_al:LIPIcs:2016:6553,
  author =	{Tomer Kotek and Helmut Veith and Florian Zuleger},
  title =	{{Monadic Second Order Finite Satisfiability and Unbounded Tree-Width}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Jean-Marc Talbot and Laurent Regnier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6553},
  URN =		{urn:nbn:de:0030-drops-65537},
  doi =		{10.4230/LIPIcs.CSL.2016.13},
  annote =	{Keywords: Monadic Second Order Logic MSO, Two variable Fragment with Counting C2, Finite decidability, Unbounded Tree-width, WS1S with Cardinality Constraints}
}

Keywords: Monadic Second Order Logic MSO, Two variable Fragment with Counting C2, Finite decidability, Unbounded Tree-width, WS1S with Cardinality Constraints
Collection: 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)
Issue Date: 2016
Date of publication: 29.08.2016

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