Undecidability of theories of semirings with fixed points

2025/12/22 by Anupam Das, Das, Anupam, Abhishek De +3
Computer Science · #Advanced Algebra and Logic #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems

paper · doi:10.48550/arxiv.2512.19401

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

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 inseperability. Our result applies to many theories proposed in the literature, including Conway μ-semirings, Park μ-semirings, and Chomsky algebras.

Citations

• Commutative Action Logic
• Action Logic is Undecidable

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