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URN: urn:nbn:de:0030-drops-39438
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Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable

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Abstract

We consider the quantifier alternation hierarchy within two-variable first-order logic FO^2[<,suc] over finite words with linear order and binary successor predicate. We give a single identity of omega-terms for each level of this hierarchy. This shows that for a given regular language and a non-negative integer~$m$ it is decidable whether the language is definable by a formula in FO^2[<,suc] which has at most m quantifier alternations. We also consider the alternation hierarchy of unary temporal logic TL[X,F,Y,P] defined by the maximal number of nested negations. This hierarchy coincides with the FO^2[<,suc] quantifier alternation hierarchy.

BibTeX - Entry

@InProceedings{kufleitner_et_al:LIPIcs:2013:3943,
  author =	{Manfred Kufleitner and Alexander Lauser},
  title =	{{Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{305--316},
  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/2013/3943},
  URN =		{urn:nbn:de:0030-drops-39438},
  doi =		{10.4230/LIPIcs.STACS.2013.305},
  annote =	{Keywords: automata theory, semigroups, regular languages, first-order logic}
}

Keywords: automata theory, semigroups, regular languages, first-order logic
Seminar: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue date: 2013
Date of publication: 2013


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