Definability equals recognizability for graphs of bounded treewidth
Logic in Computer Science
2016-05-11 v1 Computational Complexity
Discrete Mathematics
Data Structures and Algorithms
Formal Languages and Automata Theory
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
Cite
@article{arxiv.1605.03045,
title = {Definability equals recognizability for graphs of bounded treewidth},
author = {Mikołaj Bojańczyk and Michał Pilipczuk},
journal= {arXiv preprint arXiv:1605.03045},
year = {2016}
}
Comments
21 pages, an extended abstract will appear in the proceedings of LICS 2016