A profinite approach to complete bifix decodings of recurrent languages

A seminal paper published in 2012 by Berstel et al. in the Journal of Algebra initiated the systematic study of intersections of recurrent languages and complete bifix codes. One of the main results of this line of research, obtained in 2015 by Berthé et al., states that if $F$ is a uniformly recurrent dendric language (for example, a Sturmian language), then every complete bifix decoding of $F$ is also uniformly recurrent dendric. A delicate part of the proof is showing that the decoding is indeed uniformly recurrent. We introduce a method, relying on the free profinite monoid, giving a new proof of that part, and in fact a significant generalization based on the notion of $F$-charged bifix code.

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Alfredo Costa

Speaker's Institution




Semigroups, Automata and Languages