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Compact Labelings For Efficient First-Order Model-Checking

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 نشر من قبل Mamadou Moustapha Kant\\'e
 تاريخ النشر 2014
  مجال البحث الهندسة المعلوماتية
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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 emph{nicely locally cwd-decomposable}. This notion generalizes that of a emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded emph{clique-width} with limited overlaps. We also consider such labelings for emph{bounded} first-order formulas on graph classes of emph{bounded expansion}. Some of these results are extended to counting queries.



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