LIPIcs.FSTTCS.2010.13.pdf
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Special tree-width and the verification of monadic second-order graph pr operties
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2010-12-14
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Bruno Courcelle. Special tree-width and the verification of monadic second-order graph pr operties. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 13-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.FSTTCS.2010.13
https://doi.org/10.4230/LIPIcs.FSTTCS.2010.13
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.
Keywords
- model-checking
- monadic second-order logic
- fixed-parameter tractability
- special tree-width
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