MSO Undecidability for Hereditary Classes of Unbounded Clique Width

Authors Anuj Dawar , Abhisekh Sankaran

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Anuj Dawar
  • Department of Computer Science and Technology, University of Cambridge, UK
Abhisekh Sankaran
  • Department of Computer Science and Technology, University of Cambridge, UK

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Anuj Dawar and Abhisekh Sankaran. MSO Undecidability for Hereditary Classes of Unbounded Clique Width. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Seese’s conjecture for finite graphs states that monadic second-order logic (MSO) is undecidable on all graph classes of unbounded clique-width. We show that to establish this it would suffice to show that grids of unbounded size can be interpreted in two families of graph classes: minimal hereditary classes of unbounded clique-width; and antichains of unbounded clique-width under the induced subgraph relation. We explore all the currently known classes of the former category and establish that grids of unbounded size can indeed be interpreted in them.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
  • clique width
  • Seese’s conjecture
  • antichain
  • MSO interpretation
  • grid


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