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DOI: 10.4230/LIPIcs.MFCS.2016.66

Two-Variable Logic over Countable Linear Orderings

Authors: Amaldev Manuel and A. V. Sreejith

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract

We study the class of languages of finitely-labelled countable linear orderings definable in two-variable first-order logic. We give a number of characterisations, in particular an algebraic one in terms of circle monoids, using equations. This generalises the corresponding characterisation, namely variety DA, over finite words to the countable case. A corollary is that the membership in this class is decidable: for instance given an MSO formula it is possible to check if there is an equivalent two-variable logic formula over countable linear orderings. In addition, we prove that the satisfiability problems for two-variable logic over arbitrary, countable, and scattered linear orderings are NEXPTIME-complete.

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Amaldev Manuel and A. V. Sreejith. Two-Variable Logic over Countable Linear Orderings. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 66:1-66:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{manuel_et_al:LIPIcs.MFCS.2016.66,
  author =	{Manuel, Amaldev and Sreejith, A. V.},
  title =	{{Two-Variable Logic over Countable Linear Orderings}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{66:1--66:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.66},
  URN =		{urn:nbn:de:0030-drops-64788},
  doi =		{10.4230/LIPIcs.MFCS.2016.66},
  annote =	{Keywords: circ-monoids, countable linear orderings, FO^2}
}

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Two-Variable Logic over Countable Linear Orderings

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