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From Sets to Points: Simplifying MSO Interpretations via Reparameterizations

Author Alexander Rabinovich

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Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Models of computation
Keywords
  • Monadic Second-Order Logic
  • MSO interpretation
  • interpretation simplification
  • reparameterization
  • decidability

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Abstract

We study the conditions under which monadic second-order (MSO) interpretations can be simplified by replacing representations of elements as tuples of arbitrary sets with representations as tuples of finite sets or points. Using reparameterizations of MSO formulas, we prove that for formulas with free finite-set variables, it is decidable whether a point reparameterization exists, and that such a reparameterization can be effectively constructed over countable chains. Moreover, over countable Dedekind-complete labeled chains, a formula with free arbitrary set variables admits a finite-set reparameterization if and only if it has at most countably many satisfying assignments. These results yield effective simplification procedures for MSO interpretations over broad classes of countable linear orders.

Cite As Get BibTex

Alexander Rabinovich. From Sets to Points: Simplifying MSO Interpretations via Reparameterizations. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 189:1-189:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.189

Author Details

Alexander Rabinovich
  • Blavatnik School of Computer Science and Artificial Intelligence, Tel Aviv University, Israel

Funding

  • Rabinovich, Alexander: Supported in part by Len Blavatnik and the Blavatnik Family foundation.

Acknowledgements

I would like to thank the reviewers for their careful reading and valuable comments.

References

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