A profinite approach to complete bifix decodings of recurrent languages
Combinatorics
2025-09-04 v2 Dynamical Systems
Group Theory
Abstract
We approach the study of complete bifix decodings of (uniformly) recurrent languages with the help of the free profinite monoid. We show that the complete bifix decoding of a uniformly recurrent language by an -charged rational complete bifix code is uniformly recurrent. An analogous result is obtained for recurrent languages.
Keywords
Cite
@article{arxiv.2208.11768,
title = {A profinite approach to complete bifix decodings of recurrent languages},
author = {Alfredo Costa},
journal= {arXiv preprint arXiv:2208.11768},
year = {2025}
}
Comments
Original Manuscript of article to be published by De Gruyter in Forum Mathematicum. The last section of the version in Forum Mathematicum is very different, as there it is not proved that the Sch\"utzenberger group is an invariant of eventual conjugacy (the argument in the Original Manuscript had a flaw), but only that its maximal pronilpotent quotient is invariant by eventual conjugacy