On Canonical Models for Rational Functions over Infinite Words

Authors Emmanuel Filiot, Olivier Gauwin, Nathan Lhote, Anca Muscholl

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Emmanuel Filiot
  • Université Libre de Bruxelles, Belgium
Olivier Gauwin
  • LaBRI, Université de Bordeaux, France
Nathan Lhote
  • LaBRI, Université de Bordeaux, France and Université Libre de Bruxelles, Belgium
Anca Muscholl
  • LaBRI, Université de Bordeaux, France

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Emmanuel Filiot, Olivier Gauwin, Nathan Lhote, and Anca Muscholl. On Canonical Models for Rational Functions over Infinite Words. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


This paper investigates canonical transducers for rational functions over infinite words, i.e., functions of infinite words defined by finite transducers. We first consider sequential functions, defined by finite transducers with a deterministic underlying automaton. We provide a Myhill-Nerode-like characterization, in the vein of Choffrut's result over finite words, from which we derive an algorithm that computes a transducer realizing the function which is minimal and unique (up to the automaton for the domain). The main contribution of the paper is the notion of a canonical transducer for rational functions over infinite words, extending the notion of canonical bimachine due to Reutenauer and Schützenberger from finite to infinite words. As an application, we show that the canonical transducer is aperiodic whenever the function is definable by some aperiodic transducer, or equivalently, by a first-order transduction. This allows to decide whether a rational function of infinite words is first-order definable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
  • transducers
  • infinite words
  • minimization
  • aperiodicty
  • first-order logic


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