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Single-Use Automata and Transducers for Infinite Alphabets

Authors Mikołaj Bojańczyk, Rafał Stefański

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Author Details

Mikołaj Bojańczyk
  • Institute of Informatics, University of Warsaw, Poland
Rafał Stefański
  • Institute of Informatics, University of Warsaw, Poland

Funding

Supported by the European Research Council under the European Unions Horizon 2020 research and innovation programme (ERC consolidator grant LIPA, agreement no. 683080).

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Mikołaj Bojańczyk and Rafał Stefański. Single-Use Automata and Transducers for Infinite Alphabets. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 113:1-113:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.113

Abstract

Our starting point are register automata for data words, in the style of Kaminski and Francez. We study the effects of the single-use restriction, which says that a register is emptied immediately after being used. We show that under the single-use restriction, the theory of automata for data words becomes much more robust. The main results are: (a) five different machine models are equivalent as language acceptors, including one-way and two-way single-use register automata; (b) one can recover some of the algebraic theory of languages over finite alphabets, including a version of the Krohn-Rhodes Theorem; (c) there is also a robust theory of transducers, with four equivalent models, including two-way single use transducers and a variant of streaming string transducers for data words. These results are in contrast with automata for data words without the single-use restriction, where essentially all models are pairwise non-equivalent.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Automata
  • semigroups
  • data words
  • orbit-finite sets

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