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Undecidability for Semirings with Fixed Points

Authors Anupam Das , Abhishek De , Stepan L. Kuznetsov

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Subject Classification

ACM Subject Classification
  • Theory of computation → Grammars and context-free languages
  • Theory of computation → Algebraic language theory
  • Theory of computation → Logic and verification
Keywords
  • Semirings
  • fixed points
  • decidability
  • context-free
  • inseparability

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Abstract

In this work, we prove the undecidability (and Σ⁰₁-completeness) of several theories of semirings with fixed points. The generality of our results stems from recursion theoretic methods, namely the technique of effective inseparability. Our result applies to many theories proposed in the literature, including Conway μ-semirings, Park μ-semirings, and Chomsky algebras.

Cite As Get BibTex

Anupam Das, Abhishek De, and Stepan L. Kuznetsov. Undecidability for Semirings with Fixed Points. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FSCD.2026.15

Author Details

Anupam Das
  • University of Birmingham, UK
Abhishek De
  • Krea University, India
Stepan L. Kuznetsov
  • Steklov Mathematical Institute of RAS, Russia

Funding

  • Das, Anupam: This author has been supported by a UKRI Future Leaders Fellowship, Structure vs Invariants in Proofs, project number MR/S035540/1.
  • De, Abhishek: This author has been supported by a UKRI Future Leaders Fellowship, Structure vs Invariants in Proofs, project number MR/S035540/1.
  • Kuznetsov, Stepan L.: The work of this author was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2025-303).

References

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