Definability equals recognizability for graphs of bounded treewidth

Mikołaj Bojańczyk; Michał Pilipczuk

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arXiv · 1605.03045

Definability equals recognizability for graphs of bounded treewidth

Mikołaj Bojańczyk·Michał Pilipczuk

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Abstract

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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Mikołaj Bojańczyk, Michał Pilipczuk. 2016-05-10. Definability equals recognizability for graphs of bounded treewidth. https://arxiv.org/abs/1605.03045

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