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Reversible Transducers over Infinite Words

Authors Luc Dartois , Paul Gastin , Loïc Germerie Guizouarn , R. Govind , Shankaranarayanan Krishna

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ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • Transducers
  • Regular functions
  • Reversibility
  • Composition
  • SSTs

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Abstract

Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to synthesis, where transformation specifications are converted into equivalent transducers. These specifications are presented in a modular way, and composing the resultant machines simulates the full specification. An important result by Dartois et al. [Luc Dartois et al., 2017] shows that composition of two-way transducers enjoy a polynomial composition when the underlying transducer is reversible, that is, if they are both deterministic and co-deterministic. This is a major improvement over general deterministic two-way transducers, for which composition causes a doubly exponential blow-up in the size of the inputs in general. Moreover, they show that reversible two-way transducers have the same expressiveness as deterministic two-way transducers. However, the notion of reversible two-way transducers over infinite words as well as the question of their expressiveness were not studied yet.
In this article, we introduce the class of reversible two-way transducers over infinite words and show that they enjoy the same expressive power as deterministic two-way transducers over infinite words. This is done through a non-trivial, effective construction inducing a single exponential blow-up in the set of states. Further, we also prove that composing two reversible two-way transducers over infinite words incurs only a polynomial complexity, thereby providing an efficient procedure for composition of transducers over infinite words.

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Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna. Reversible Transducers over Infinite Words. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CONCUR.2024.21

Author Details

Luc Dartois
  • Université Paris Est Creteil, LACL, F-94010 Créteil, France
Paul Gastin
  • Université Paris-Saclay, ENS Paris-Saclay, CNRS, LMF, 91190, Gif-sur-Yvette, France
  • CNRS, ReLaX, IRL 2000, Siruseri, India
Loïc Germerie Guizouarn
  • Université Paris Est Creteil, LACL, F-94010 Créteil, France
R. Govind
  • Uppsala University, Sweden
Shankaranarayanan Krishna
  • Indian Institute of Technology Bombay, Mumbai, India

References

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