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..

PDF Abstract
No code implementations yet. Submit your code now

Categories


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

Datasets


  Add Datasets introduced or used in this paper