License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2016.17
URN: urn:nbn:de:0030-drops-65575
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6557/
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Elberfeld, Michael

Context-Free Graph Properties via Definable Decompositions

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LIPIcs-CSL-2016-17.pdf (0.4 MB)

Abstract

Monadic-second order logic (MSO-logic) is successfully applied in both language theory and algorithm design. In the former, properties definable by MSO-formulas are exactly the regular properties on many structures like, most prominently, strings. In the latter, solving a problem for structures of bounded tree width is routinely done by defining it in terms of an MSO-formula and applying general formula-evaluation procedures like Courcelle's. The present paper furthers the study of second-order logics with close connections to language theory and algorithm design beyond MSO-logic.

We introduce a logic that allows to expand a given structure with an existentially quantified tree decomposition of bounded width and test an MSO-definable property for the resulting expanded structure. It is proposed as a candidate for capturing the notion of "context-free graph properties" since it corresponds to the context-free languages on strings, has the same closure properties, and an alternative definition similar to the one of Chomsky and Schützenberger for context-free languages. Besides studying its language-theoretic aspects, we consider its expressive power as well as the algorithmics of its satisfiability and evaluation problems.

BibTeX - Entry

@InProceedings{elberfeld:LIPIcs:2016:6557,
  author =	{Michael Elberfeld},
  title =	{{Context-Free Graph Properties via Definable Decompositions}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Jean-Marc Talbot and Laurent Regnier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6557},
  URN =		{urn:nbn:de:0030-drops-65575},
  doi =		{10.4230/LIPIcs.CSL.2016.17},
  annote =	{Keywords: finite model theory, monadic second-order logic,  tree decomposition,  context-free languages,  expressive power}
}

Keywords: finite model theory, monadic second-order logic, tree decomposition, context-free languages, expressive power
Collection: 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)
Issue Date: 2016
Date of publication: 29.08.2016

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