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Bibliographic Details
Main Authors: Filmus, Yuval, Makowsky, Johann A.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.02771
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author Filmus, Yuval
Makowsky, Johann A.
author_facet Filmus, Yuval
Makowsky, Johann A.
contents Courcelle's Theorem states that on graphs $G$ of tree-width at most $k$ with a given tree-decomposition of size $t(G)$, graph properties $\mathcal{P}$ definable in Monadic Second Order Logic can be checked in linear time in the size of $t(G)$. Inspired by L. Lovász' work using connection matrices instead of logic, we give a generalized version of Courcelle's theorem which replaces the definability hypothesis by a purely combinatorial hypothesis using a generalization of connection matrices.
format Preprint
id arxiv_https___arxiv_org_abs_2505_02771
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Courcelle's Theorem Without Logic
Filmus, Yuval
Makowsky, Johann A.
Logic in Computer Science
05C85, 03C13, 68R10
Courcelle's Theorem states that on graphs $G$ of tree-width at most $k$ with a given tree-decomposition of size $t(G)$, graph properties $\mathcal{P}$ definable in Monadic Second Order Logic can be checked in linear time in the size of $t(G)$. Inspired by L. Lovász' work using connection matrices instead of logic, we give a generalized version of Courcelle's theorem which replaces the definability hypothesis by a purely combinatorial hypothesis using a generalization of connection matrices.
title Courcelle's Theorem Without Logic
topic Logic in Computer Science
05C85, 03C13, 68R10
url https://arxiv.org/abs/2505.02771