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Definability equals recognizability for graphs of bounded treewidth (1605.03045v1)
Published 10 May 2016 in cs.LO, cs.CC, cs.DM, cs.DS, and cs.FL
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