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
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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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