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A profinite approach to complete bifix decodings of recurrent languages

  • Alfredo Costa ORCID logo EMAIL logo
Published/Copyright: June 29, 2023

Abstract

We approach the study of complete bifix decodings of (uniformly) recurrent languages with the help of free profinite monoids. We show that the complete bifix decoding of a uniformly recurrent language F by an F-charged rational complete bifix code is uniformly recurrent. An analogous result is obtained for recurrent languages. As an application of the machinery developed within this approach, we show that the maximal pronilpotent quotient of the Schützenberger group of an irreducible symbolic dynamical system is an invariant of eventual conjugacy.


Communicated by Manfred Droste


Award Identifier / Grant number: SFRH/BSAB/150401/2019

Award Identifier / Grant number: UIDB/00324/2020

Funding statement: This work was supported by the sabbatical scholarship SFRH/BSAB/150401/2019 of the Portuguese Foundation for Science and Technology (FCT), and by the Centre for Mathematics of the University of Coimbra, under grant UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES.

Acknowledgements

This work was carried out in part during a sabbatical leave at City College of New York, CUNY, whose hospitality is gratefully acknowledged. The author is grateful to Herman Goulet-Ouellet for carefully reading this paper and detecting the flaw, in one of its preliminary versions, that is mentioned right after the statement of Problem 10.2. The author also thanks the referee for his/her important work.

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Received: 2022-08-27
Revised: 2023-02-20
Published Online: 2023-06-29
Published in Print: 2023-07-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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