EUDML

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Multi-dimensional sets recognizable in all abstract numeration systems

Émilie Charlier; Anne Lacroix; Narad Rampersad — 2012

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We prove that the subsets of that are -recognizable for all abstract numeration systems are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.

A Characterization of Multidimensional $S$ -Automatic Sequences

Emilie Charlier; Tomi Kärki; Michel Rigo — 2009

Actes des rencontres du CIRM

An infinite word is $S$ -automatic if, for all $n \geq 0$ , its $(n + 1)$ st letter is the output of a deterministic automaton fed with the representation of $n$ in the considered numeration system $S$ . In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for $d \geq 2$ , we state that a multidimensional infinite word $x : ℕ^{d} \to Σ$ over a finite alphabet $Σ$ is $S$ -automatic for some abstract numeration...