License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2010.13
URN: urn:nbn:de:0030-drops-28494
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2849/
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Courcelle, Bruno

Special tree-width and the verification of monadic second-order graph pr operties

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Abstract

The model-checking problem for monadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite deterministic automata from monadic second-order sentences, but this computation produces automata of hyper-exponential sizes, and this is not avoidable. To overcome this difficulty, we propose to consider particular monadic second-order graph properties that are nevertheless interesting for Graph Theory and to interpret automata instead of trying to compile them (joint work with I. Durand).

For checking monadic second-order sentences written with edge set quantifications, the appropriate parameter is tree-width. We introduce special tree-width, a graph complexity measure between path-width and tree-width. The corresponding automata are easier to construct than those for tree-width.

BibTeX - Entry

@InProceedings{courcelle:LIPIcs:2010:2849,
  author =	{Bruno Courcelle},
  title =	{{Special tree-width and the verification of monadic second-order graph pr operties}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{13--29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Kamal Lodaya and Meena Mahajan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2849},
  URN =		{urn:nbn:de:0030-drops-28494},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.13},
  annote =	{Keywords: model-checking, monadic second-order logic, fixed-parameter tractability, special tree-width}
}

Keywords: model-checking, monadic second-order logic, fixed-parameter tractability, special tree-width
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)
Issue Date: 2010
Date of publication: 14.12.2010

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