Pebble Transducers with Unary Output

Author Gaëtan Douéneau-Tabot

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Gaëtan Douéneau-Tabot
  • IRIF, Université de Paris, France


The author is grateful to Olivier Carton for discussing about this work. He also thanks the reviewers for their helpful comments and remarks.

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Gaëtan Douéneau-Tabot. Pebble Transducers with Unary Output. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Bojańczyk recently initiated an intensive study of deterministic pebble transducers, which are two-way automata that can drop marks (named "pebbles") on their input word, and produce an output word. They describe functions from words to words. Two natural restrictions of this definition have been investigated: marble transducers by Douéneau-Tabot et al., and comparison-free pebble transducers (that we rename here "blind transducers") by Nguyên et al. Here, we study the decidability of membership problems between the classes of functions computed by pebble, marble and blind transducers that produce a unary output. First, we show that pebble and marble transducers have the same expressive power when the outputs are unary (which is false over non-unary outputs). Then, we characterize 1-pebble transducers with unary output that describe a function computable by a blind transducer, and show that the membership problem is decidable. These results can be interpreted in terms of automated simplification of programs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
  • polyregular functions
  • pebble transducers
  • marble transducers
  • streaming string transducers
  • factorization forests


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