Document Open Access Logo

Reversible Transducers over Infinite Words

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

PDF
Thumbnail PDF

File

LIPIcs.CONCUR.2024.21.pdf
  • Filesize: 1.02 MB
  • 22 pages

Document Identifiers

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

Cite As Get BibTex

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

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.

Subject Classification

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Rajeev Alur, Emmanuel Filiot, and Ashutosh Trivedi. Regular transformations of infinite strings. In Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science, LICS 2012, Dubrovnik, Croatia, June 25-28, 2012, pages 65-74. IEEE Computer Society, 2012. URL: https://doi.org/10.1109/LICS.2012.18.
  2. Rajeev Alur, Adam Freilich, and Mukund Raghothaman. Regular combinators for string transformations. In Thomas A. Henzinger and Dale Miller, editors, Joint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic (CSL) and the 29th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS '14, Vienna, Austria, July 14 - 18, 2014, pages 9:1-9:10. ACM, 2014. Google Scholar
  3. Nicolas Baudru and Pierre-Alain Reynier. From two-way transducers to regular function expressions. In Mizuho Hoshi and Shinnosuke Seki, editors, 22nd International Conference on Developments in Language Theory, DLT 2018, volume 11088 of Lecture Notes in Computer Science, pages 96-108. Springer, 2018. Google Scholar
  4. Udi Boker. Why These Automata Types? In Gilles Barthe, Geoff Sutcliffe, and Margus Veanes, editors, LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Awassa, Ethiopia, 16-21 November 2018, volume 57 of EPiC Series in Computing, pages 143-163. EasyChair, 2018. URL: https://doi.org/10.29007/C3BJ.
  5. Olivier Carton and Gaëtan Douéneau-Tabot. Continuous rational functions are deterministic regular. In Stefan Szeider, Robert Ganian, and Alexandra Silva, editors, 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022, August 22-26, 2022, Vienna, Austria, volume 241 of LIPIcs, pages 28:1-28:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.MFCS.2022.28.
  6. Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter. Deterministic regular functions of infinite words. In Kousha Etessami, Uriel Feige, and Gabriele Puppis, editors, 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023, July 10-14, 2023, Paderborn, Germany, volume 261 of LIPIcs, pages 121:1-121:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPICS.ICALP.2023.121.
  7. Arthur Cayley. A theorem of trees. Quarterly Journal of Mathematics, 23:376-378, 1889. URL: https://books.google.fr/books?id=M7c4AAAAIAAJ.
  8. Krishnendu Chatterjee, Thomas A. Henzinger, and Nir Piterman. Generalized Parity Games. In Helmut Seidl, editor, Foundations of Software Science and Computational Structures, pages 153-167, Berlin, Heidelberg, 2007. Springer. URL: https://doi.org/10.1007/978-3-540-71389-0_12.
  9. Bruno Courcelle. Monadic second-order definable graph transductions: A survey. Theor. Comput. Sci., 126(1):53-75, 1994. Google Scholar
  10. Luc Dartois, Paulin Fournier, Ismaël Jecker, and Nathan Lhote. On reversible transducers. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 113:1-113:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ICALP.2017.113.
  11. Luc Dartois, Paul Gastin, R. Govind, and Shankara Narayanan Krishna. Efficient construction of reversible transducers from regular transducer expressions. In Christel Baier and Dana Fisman, editors, LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer Science, Haifa, Israel, August 2 - 5, 2022, pages 50:1-50:13. ACM, 2022. URL: https://doi.org/10.1145/3531130.3533364.
  12. Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, and Shankaranarayanan Krishna. Reversible transducers over infinite words, 2024. URL: https://arxiv.org/abs/2406.11488.
  13. Luc Dartois, Paul Gastin, and Shankara Narayanan Krishna. Sd-regular transducer expressions for aperiodic transformations. In 36th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2021, Rome, Italy, June 29 - July 2, 2021, pages 1-13. IEEE, 2021. URL: https://doi.org/10.1109/LICS52264.2021.9470738.
  14. Luc Dartois, Ismaël Jecker, and Pierre-Alain Reynier. Aperiodic string transducers. In Developments in Language Theory - 20th International Conference, DLT 2016, Montréal, Canada, July 25-28, 2016, Proceedings, pages 125-137, 2016. URL: https://doi.org/10.1007/978-3-662-53132-7_11.
  15. Vrunda Dave, Emmanuel Filiot, Shankara Narayanan Krishna, and Nathan Lhote. Synthesis of computable regular functions of infinite words. Log. Methods Comput. Sci., 18(2), 2022. URL: https://doi.org/10.46298/LMCS-18(2:23)2022.
  16. Vrunda Dave, Paul Gastin, and Shankara Narayanan Krishna. Regular Transducer Expressions for Regular Transformations. In Martin Hofmann, Anuj Dawar, and Erich Grädel, editors, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic In Computer Science (LICS'18), pages 315-324, Oxford, UK, July 2018. ACM Press. Google Scholar
  17. Joost Engelfriet and Hendrik Jan Hoogeboom. MSO definable string transductions and two-way finite-state transducers. ACM Transactions on Computational Logic, 2(2):216-254, 2001. URL: https://doi.org/10.1145/371316.371512.
  18. Dominique Perrin and Jean-Eric Pin. Infinite Words: Automata, Semigroups, Logic and Games, volume 141. Elsevier, 2004. Google Scholar
  19. John C. Shepherdson. The reduction of two-way automata to one-way automata. IBM J. Res. Dev., 3(2):198-200, 1959. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact