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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2011.218
URN: urn:nbn:de:0030-drops-32333
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3233/
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Eickmeyer, Kord

Non-Definability Results for Randomised First-Order Logic

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Abstract

We investigate the expressive power of randomised first-order logic (BPFO) on restricted classes of structures. While BPFO is stronger than FO in general, even on structures with a built-in addition relation, we show that BPFO is not stronger than FO on structures with a unary vocabulary, nor on the class of equivalence relations. The same techniques can be applied to show that evenness of a linear order, and therefore graph connectivity, can not be defined in BPFO. Finally, we show that there is an FO[<]-definable query on word structures which can not be defined in BPFO[+1].

BibTeX - Entry

@InProceedings{eickmeyer:LIPIcs:2011:3233,
  author =	{Kord Eickmeyer},
  title =	{{Non-Definability Results for Randomised First-Order Logic}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{218--232},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Marc Bezem},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3233},
  URN =		{urn:nbn:de:0030-drops-32333},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2011.218},
  annote =	{Keywords: descriptive complexity, randomised logics, derandomisation}
}

Keywords: descriptive complexity, randomised logics, derandomisation
Seminar: Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL
Issue Date: 2011
Date of publication: 31.08.2011


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