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

Author Bruno Courcelle

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Bruno Courcelle

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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)


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.
  • model-checking
  • monadic second-order logic
  • fixed-parameter tractability
  • special tree-width


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