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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

Acknowledgements

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) https://doi.org/10.4230/LIPIcs.ICALP.2022.120

Abstract

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
Keywords
  • polyregular functions
  • pebble transducers
  • rational series
  • factorization forests
  • Cauchy product
  • Hadamard product

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