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 recognize...

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Bibliographic Details
Published in:Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science pp. 407 - 416
Main Authors: Bojańczyk, Mikołaj, Pilipczuk, Michał
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 05.07.2016
Series:ACM Conferences
Subjects:
Theory of computation > Logic
Monadic Second-Order Logic
treewidth
recognizability
tree decomposition
Simon's factorization forest
ISBN:9781450343916, 1450343910
Online Access:Get full text
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Summary: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.
ISBN:9781450343916
1450343910
DOI:10.1145/2933575.2934508