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DOI: 10.4230/LIPIcs.STACS.2013.317
URN: urn:nbn:de:0030-drops-39449
URL: http://drops.dagstuhl.de/opus/volltexte/2013/3944/
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Szwast, Wieslaw ; Tendera, Lidia

FO^2 with one transitive relation is decidable

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Abstract

We show that the satisfiability problem for the two-variable first-order logic, FO^2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO^2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO^2-logics over transitive structures with respect to decidability. We show that the satisfiability problem is in 2-NExpTime. Decidability of the finite satisfiability problem remains open.

BibTeX - Entry

@InProceedings{szwast_et_al:LIPIcs:2013:3944,
  author =	{Wieslaw Szwast and Lidia Tendera},
  title =	{{FO^2 with one transitive relation is decidable}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{317--328},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3944},
  URN =		{urn:nbn:de:0030-drops-39449},
  doi =		{10.4230/LIPIcs.STACS.2013.317},
  annote =	{Keywords: classical decision problem, two-variable first-order logic, decidability, computational complexity}
}

Keywords: classical decision problem, two-variable first-order logic, decidability, computational complexity
Seminar: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 18.02.2013


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