[en] The language of a numeration system is the set of all words that are the representation of an integer in this system. The regularity of such a language is a desirable property of the associated numeration system as it is necessary for various results of first order logic and automata theory, such as the ability to use Walnut to prove results automatically.
Deciding whether the language of a given greedy numeration system is regular is a question that was investigated by Hollander in a 1998 article. However, this article focuses on the case of dominant root numeration systems, where Hollander then uses a link to Rényi numeration systems to prove his results.
Motivated by the recent introduction of alternate bases and the procurement of a result linking these systems to greedy numeration systems without a dominant root, we extend the results of Hollander and find criteria to decide the regularity of the associated language of all greedy numeration systems.
Joint work with Émilie Charlier.
