Courcelle's Theorem Without Logic
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912361498017792 |
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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 |