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Deterministic Regular Functions of Infinite Words

Authors Olivier Carton , Gaëtan Douéneau-Tabot, Emmanuel Filiot , Sarah Winter

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Author Details

Olivier Carton
  • Université Paris Cité, CNRS, IRIF, F-75013, France
  • Institut Universitaire de France, Paris, France
Gaëtan Douéneau-Tabot
  • Université Paris Cité, CNRS, IRIF, F-75013, France
  • Direction générale de l'armement - Ingénierie des projets, Paris, France
Emmanuel Filiot
  • Université libre de Bruxelles & F.R.S.-FNRS, Brussels, Belgium
Sarah Winter
  • Université libre de Bruxelles & F.R.S.-FNRS, Brussels, Belgium

Funding

This work was partially supported by the Fonds National de la Recherche Scientifique - F.R.S.-FNRS - under the MIS project F451019F.

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Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter. Deterministic Regular Functions of Infinite Words. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 121:1-121:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICALP.2023.121

Abstract

Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller streaming string transducers, and to functions defined by MSO-transductions. Regular functions are however not computable in general (for a classical extension of Turing computability to infinite inputs), and we consider in this paper the class of deterministic regular functions of infinite words, realized by deterministic two-way transducers without look-ahead. We prove that it is a well-behaved class of functions: they are computable, closed under composition, characterized by the guarded fragment of MSO-transductions, by deterministic Büchi streaming string transducers, by deterministic two-way transducers with finite look-ahead, and by finite compositions of sequential functions and one fixed basic function called map-copy-reverse.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • infinite words
  • streaming string transducers
  • two-way transducers
  • monadic second-order logic
  • look-aheads
  • factorization forests

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References

  1. Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman. A general theory of translation. Mathematical Systems Theory, 3(3):193-221, 1969. Google Scholar
  2. Rajeev Alur and Pavol Cerný. Expressiveness of streaming string transducers. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, volume 8 of LIPIcs, pages 1-12. Schloss Dagstuhl, 2010. Google Scholar
  3. 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, pages 65-74. IEEE Computer Society, 2012. Google Scholar
  4. Rajeev Alur, Adam Freilich, and Mukund Raghothaman. Regular combinators for string transformations. In Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), page 9. ACM, 2014. Google Scholar
  5. Nicolas Baudru and Pierre-Alain Reynier. From two-way transducers to regular function expressions. In International Conference on Developments in Language Theory, pages 96-108. Springer, 2018. Google Scholar
  6. Mikołaj Bojańczyk and Rafał Stefański. Single-use automata and transducers for infinite alphabets. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020. Google Scholar
  7. Mikołaj Bojańczyk. Polyregular Functions, 2018. URL: https://doi.org/10.48550/arXiv.1810.08760.
  8. J. R. Büchi. Weak second-order arithmetic and finite automata. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 6(1-6):66-92, 1960. Google Scholar
  9. Olivier Carton and Gaëtan Douéneau-Tabot. Continuous rational functions are deterministic regular. In 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022, 2022. Google Scholar
  10. Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter. Deterministic regular functions of infinite words. CoRR, abs/2302.06672, 2023. URL: https://doi.org/10.48550/arXiv.2302.06672.
  11. Michal P. Chytil and Vojtěch Jákl. Serial composition of 2-way finite-state transducers and simple programs on strings. In 4th International Colloquium on Automata, Languages, and Programming, ICALP 1977, pages 135-147. Springer, 1977. Google Scholar
  12. Thomas Colcombet. A combinatorial theorem for trees. In 34th International Colloquium on Automata, Languages, and Programming, ICALP 2007, 2007. Google Scholar
  13. Bruno Courcelle. Monadic second-order definable graph transductions: A survey. Theor. Comput. Sci., 126:53-75, 1994. Google Scholar
  14. Bruno Courcelle and Joost Engelfriet. Graph structure and monadic second-order logic: a language-theoretic approach, volume 138. Cambridge University Press, 2012. Google Scholar
  15. Luc Dartois, Emmanuel Filiot, and Nathan Lhote. Logics for word transductions with synthesis. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, pages 295-304. ACM, 2018. Google Scholar
  16. Luc Dartois, Paulin Fournier, Ismaël Jecker, and Nathan Lhote. On reversible transducers. In 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, volume 80 of LIPIcs, pages 113:1-113:12. Schloss Dagstuhl, 2017. Google Scholar
  17. Luc Dartois, Ismaël Jecker, and Pierre-Alain Reynier. Aperiodic string transducers. Int. J. Found. Comput. Sci., 29(5):801-824, 2018. Google Scholar
  18. Vrunda Dave, Emmanuel Filiot, Shankara Narayanan Krishna, and Nathan Lhote. Synthesis of computable regular functions of infinite words. In 31st International Conference on Concurrency Theory (CONCUR 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020. Google Scholar
  19. 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. Google Scholar
  20. Vrunda Dave, Paul Gastin, and Shankara Narayanan Krishna. Regular transducer expressions for regular transformations. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, pages 315-324. ACM, 2018. Google Scholar
  21. C. C. Elgot. Decision problems of finite automata design and related arithmetics. In Transactions of the American Mathematical Society, 98(1):21-51, 1961. Google Scholar
  22. Joost Engelfriet and Hendrik Jan Hoogeboom. MSO definable string transductions and two-way finite-state transducers. ACM Transactions on Computational Logic (TOCL), 2(2):216-254, 2001. Google Scholar
  23. Emmanuel Filiot and Sarah Winter. Synthesizing computable functions from rational specifications over infinite words. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2021, December 15-17, 2021, Virtual Conference. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  24. Erich Grädel. On the restraining power of guards. J. Symb. Log., 64(4):1719-1742, 1999. Google Scholar
  25. Eitan M Gurari. The equivalence problem for deterministic two-way sequential transducers is decidable. SIAM Journal on Computing, 11(3):448-452, 1982. Google Scholar
  26. Dominique Perrin and Jean-Éric Pin. Infinite words: automata, semigroups, logic and games. Academic Press, 2004. Google Scholar
  27. Imre Simon. Factorization forests of finite height. Theor. Comput. Sci., 72(1):65-94, 1990. URL: https://doi.org/10.1016/0304-3975(90)90047-L.
  28. Wolfgang Thomas. Languages, automata, and logic. In Handbook of formal languages, pages 389-455. Springer, 1997. Google Scholar
  29. Boris Avraamovich Trakhtenbrot. Finite automata and logic of monadic predicates (in Russian). Dokl. Akad. Nauk SSSR, 140:326-329, 1961. Google Scholar
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