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Deterministic Regular Functions of Infinite Words

Authors Olivier Carton , Gaëtan Douéneau-Tabot, Emmanuel Filiot , Sarah Winter

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Author Details

Olivier Carton
  • Université Paris Cité, CNRS, IRIF, F-75013, France
  • Institut Universitaire de France, Paris, France
Gaëtan Douéneau-Tabot
  • Université Paris Cité, CNRS, IRIF, F-75013, France
  • Direction générale de l'armement - Ingénierie des projets, Paris, France
Emmanuel Filiot
  • Université libre de Bruxelles & F.R.S.-FNRS, Brussels, Belgium
Sarah Winter
  • Université libre de Bruxelles & F.R.S.-FNRS, Brussels, Belgium

Funding

This work was partially supported by the Fonds National de la Recherche Scientifique - F.R.S.-FNRS - under the MIS project F451019F.

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Olivier Carton, Gaëtan Douéneau-Tabot, Emmanuel Filiot, and Sarah Winter. Deterministic Regular Functions of Infinite Words. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 121:1-121:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.121

Abstract

Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller streaming string transducers, and to functions defined by MSO-transductions. Regular functions are however not computable in general (for a classical extension of Turing computability to infinite inputs), and we consider in this paper the class of deterministic regular functions of infinite words, realized by deterministic two-way transducers without look-ahead. We prove that it is a well-behaved class of functions: they are computable, closed under composition, characterized by the guarded fragment of MSO-transductions, by deterministic Büchi streaming string transducers, by deterministic two-way transducers with finite look-ahead, and by finite compositions of sequential functions and one fixed basic function called map-copy-reverse.

Subject Classification

ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • infinite words
  • streaming string transducers
  • two-way transducers
  • monadic second-order logic
  • look-aheads
  • factorization forests

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