用于高效一阶模型检验的紧凑标记
Compact Labelings For Efficient First-Order Model-Checking
摘要：
我们考虑可以从标签检查的图形属性，即，位序列，对数长度附加到顶点。我们证明了存在这样一个标签检查一个一阶公式的自由集变量在图的每一个类是\emph{nicely locally cwd-decomposable}。这个概念概括了\emph{nicely locally tree-decomposable}类的概念。这些类的图可以由具有有限重叠的有界\emph{clique-width}的图覆盖。我们也考虑这样的标签的\emph{bounded}一阶公式的图形类的\emph{bounded expansion}。其中一些结果被扩展到计数查询。
英文摘要：
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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