Definability equals recognizability for graphs of bounded treewidth

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. The talk will be based on a joint work with Mikołaj Bojańczyk, presented at LICS 2016. The preprint is available on arxiv: http: //arxiv. org/abs/1605. 03045

Authors

• Mikołaj Bojańczyk
• Michał Pilipczuk

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