Robustness of Pisot-regular sequences

[en] We consider numeration systems based on a d-tuple U=(U_1,...,U_d) of sequences of integers and we define (U,K)-regular sequences through K-recognizable formal series, where K is any semiring. We show that, for any d-tuple U of Pisot numeration systems and any commutative semiring K, this definition does not depend on the greediness of the U-representations of integers. The proof is constructive and is based on the fact that the normalization is realizable by a 2d-tape finite automaton. In particular, we use an ad hoc operation mixing a 2d-tape automaton and a K-automaton in order to obtain a new K-automaton.

Disciplines :

Mathematics

Author, co-author :

Charlier, Emilie ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Cisternino, Célia ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Stipulanti, Manon ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Language :

English

Title :

Robustness of Pisot-regular sequences

Publication date :

2021

Journal title :

Advances in Applied Mathematics

ISSN :

0196-8858

eISSN :

1090-2074

Publisher :

Elsevier, Atlanta, Georgia

Volume :

125

Pages :

102151

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 22 June 2020

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