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URN: urn:nbn:de:0030-drops-54436
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Two-variable Logic with Counting and a Linear Order

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Abstract

We study the finite satisfiability problem for the two-variable fragment of the first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in presence of two other binary symbols). In the case of one linear order it is NEXPTIME-complete, even in presence of the successor relation. Surprisingly, the complexity of the problem explodes when we add one binary symbol more: C2 with one linear order and its successor, in presence of other binary predicate symbols, is decidable, but it is as expressive (and as complex) as Vector Addition Systems.

BibTeX - Entry

@InProceedings{charatonik_et_al:LIPIcs:2015:5443,
  author =	{Witold Charatonik and Piotr Witkowski},
  title =	{{Two-variable Logic with Counting and a Linear Order}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{631--647},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Stephan Kreutzer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5443},
  URN =		{urn:nbn:de:0030-drops-54436},
  doi =		{10.4230/LIPIcs.CSL.2015.631},
  annote =	{Keywords: Two-variable logic, counting quantifiers, linear order, satisfiability, complexity}
}

Keywords: Two-variable logic, counting quantifiers, linear order, satisfiability, complexity
Seminar: 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)
Issue date: 2015
Date of publication: 2015


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