A Hierarchical Approach to Graph Automata and Monadic Second-Order Logic over Graphs
نویسنده
چکیده
A hierarchical approach to the decomposition of graphs is introduced which is related to the notion of tree decomposition. On this basis a hierarchical automaton model for graphs is deened. We show that this automaton model is (relative to an appropriate class of graphs) equivalent to monadic second-order logic in expressive power, properly strengthening previous results on monadic second-order logic over graphs. We discuss the connections with graphs of bounded tree-width. We show that existential monadic second-order logic on graphs of bounded tree-width is not closed under complement.
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A Hierarchical Approach to Monadic Second-Order Logic over Graphs
The expressiveness of existential monadic second-order logic is investigated over several classes of nite graphs among them the graphs of bounded tree-width. A hierarchical approach to the decomposition of graphs is introduced which is related to the notion of tree decomposition. Among other results we show that existential monadic second-order logic on graphs of bounded tree-width is not close...
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