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Regular Resynchronizability of Origin Transducers Is Undecidable

Authors Denis Kuperberg , Jan Martens

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Author Details

Denis Kuperberg
  • CNRS, LIP, ENS Lyon, France
Jan Martens
  • Eindhoven University of Technology, The Netherlands

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Denis Kuperberg and Jan Martens. Regular Resynchronizability of Origin Transducers Is Undecidable. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.MFCS.2020.58

Abstract

We study the relation of containment up to unknown regular resynchronization between two-way non-deterministic transducers. We show that it constitutes a preorder, and that the corresponding equivalence relation is properly intermediate between origin equivalence and classical equivalence. We give a syntactical characterization for containment of two transducers up to resynchronization, and use it to show that this containment relation is undecidable already for one-way non-deterministic transducers, and for simple classes of resynchronizations. This answers the open problem stated in recent works, asking whether this relation is decidable for two-way non-deterministic transducers.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • transducers
  • origin
  • resynchronisation
  • MSO
  • one-way
  • two-way
  • undecidability

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References

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