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Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width

Author Aliaume Lopez

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ACM Subject Classification
  • Theory of computation → Models of computation
  • Theory of computation → Automata extensions
Keywords
  • well-quasi-ordering
  • linear clique-width
  • MSO transduction
  • automata theory

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Abstract

We construct an algorithm that inputs an MSO-interpretation from finite words to graphs, and decides if there exists a k ∈ ℕ such that the class of graphs induced by the interpretation is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using {1, …, k}. In case no such k exists, we also prove that the class of graphs is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using any well-quasi-ordered set of labels. As a byproduct of our analysis, we prove that for classes of bounded linear clique-width, a weak version of a conjecture by Pouzet holds.

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Aliaume Lopez. Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.70

Author Details

Aliaume Lopez
  • University of Warsaw, Poland

Funding

  • Lopez, Aliaume: Aliaume Lopez was supported by the Polish National Science Centre (NCN) grant "Polynomial finite state computation" (2022/46/A/ST6/00072).

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