Definability equals recognizability for graphs of bounded treewidth

10 May 2016  ·  Bojańczyk Mikołaj, Pilipczuk Michał ·

We prove a conjecture of Courcelle, which states that a graph property is definable in MSO with modular counting predicates on graphs of constant treewidth if, and only if it is recognizable in the following sense: constant-width tree decompositions of graphs satisfying the property can be recognized by tree automata. While the forward implication is a classic fact known as Courcelle's theorem, the converse direction remained open..

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Logic in Computer Science Computational Complexity Discrete Mathematics Data Structures and Algorithms Formal Languages and Automata Theory


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