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Hiding Pebbles When the Output Alphabet Is Unary

Author Gaëtan Douéneau-Tabot

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Gaëtan Douéneau-Tabot
  • IRIF, Université Paris Cité & Direction générale de l'armement - Ingénierie de projets, France


The author is grateful to Olivier Carton, L{ê} Th{à}nh D{ũ}ng Nguy{ê}n and Pierre Pradic for discussing about this work.

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Gaëtan Douéneau-Tabot. Hiding Pebbles When the Output Alphabet Is Unary. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 120:1-120:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word. Blind transducers have been introduced by Nguyên et al. as a subclass of pebble transducers, which can nest two-way transducers but cannot drop pebbles on their input. In this paper, we study the classes of functions computed by pebble and blind transducers, when the output alphabet is unary. Our main result shows how to decide if a function computed by a pebble transducer can be computed by a blind transducer. We also provide characterizations of these classes in terms of Cauchy and Hadamard products, in the spirit of rational series. Furthermore, pumping-like characterizations of the functions computed by blind transducers are given.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
  • polyregular functions
  • pebble transducers
  • rational series
  • factorization forests
  • Cauchy product
  • Hadamard product


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  1. Jean Berstel and Christophe Reutenauer. Noncommutative rational series with applications, volume 137. Cambridge University Press, 2011. Google Scholar
  2. Mikolaj Bojańczyk. Polyregular functions. arXiv preprint, 2018. URL:
  3. Mikolaj Bojańczyk, Sandra Kiefer, and Nathan Lhote. String-to-string interpretations with polynomial-size output. In 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019, pages 106:1-106:14, 2019. URL:
  4. 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
  5. 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
  6. Gaëtan Douéneau-Tabot. Pebble transducers with unary output. In 46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021, August 23-27, 2021, Tallinn, Estonia, 2021. Google Scholar
  7. Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Paul Gastin. Register transducers are marble transducers. In 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, August 24-28, 2020, Prague, Czech Republic, 2020. Google Scholar
  8. Joost Engelfriet. Two-way pebble transducers for partial functions and their composition. Acta Informatica, 52(7-8):559-571, 2015. Google Scholar
  9. 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
  10. Noa Globerman and David Harel. Complexity results for two-way and multi-pebble automata and their logics. Theoretical Computer Science, 169(2):161-184, 1996. Google Scholar
  11. 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
  12. Lê Thành Dung Nguyên. Implicit automata in linear logic and categorical transducer theory. PhD thesis, Université Paris 13, 2021. Google Scholar
  13. Lê Thành Dung Nguyên, Camille Noûs, and Pierre Pradic. Comparison-free polyregular functions. In 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12-16, 2021, Glasgow, Scotland (Virtual Conference), 2021. Google Scholar
  14. John C Shepherdson. The reduction of two-way automata to one-way automata. IBM Journal of Research and Development, 3(2):198-200, 1959. Google Scholar
  15. Imre Simon. Factorization forests of finite height. Theor. Comput. Sci., 72(1):65-94, 1990. URL:
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