Register Transducers Are Marble Transducers

Authors Gaëtan Douéneau-Tabot, Emmanuel Filiot , Paul Gastin

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Author Details

Gaëtan Douéneau-Tabot
  • IRIF, Université de Paris, France
Emmanuel Filiot
  • Université libre de Bruxelles and F.R.S.-FNRS, Belgium
Paul Gastin
  • LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, France

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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). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Deterministic two-way transducers define the class of regular functions from words to words. Alur and Cerný introduced an equivalent model of transducers with registers called copyless streaming string transducers. In this paper, we drop the "copyless" restriction on these machines and show that they are equivalent to two-way transducers enhanced with the ability to drop marks, named "marbles", on the input. We relate the maximal number of marbles used with the amount of register copies performed by the streaming string transducer. Finally, we show that the class membership problems associated with these models are decidable. Our results can be interpreted in terms of program optimization for simple recursive and iterative programs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
  • streaming string transducer
  • two-way transducer
  • marbles
  • pebbles


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