Compact labelings for efficient first-order model-checking

Bruno Courcelle (), Cyril Gavoille () and Mamadou Moustapha Kanté ()
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Bruno Courcelle: Université de Bordeaux
Cyril Gavoille: Université de Bordeaux
Mamadou Moustapha Kanté: Université de Bordeaux

Journal of Combinatorial Optimization, 2011, vol. 21, issue 1, No 3, 19-46

Abstract: Abstract We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every class that is nicely locally clique-width-decomposable. This notion generalizes that of a nicely locally tree-decomposable class. The graphs of such classes can be covered by graphs of bounded clique-width with limited overlaps. We also consider such labelings for bounded first-order formulas on graph classes of bounded expansion. Some of these results are extended to counting queries.

Keywords: First-order logic; Labeling scheme; Local clique-width; Local tree-width; Locally bounded clique-width (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-009-9260-7

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