Multidimensional Generalized Automatic Sequences and Shape-symmetric Morphic Words
Formal Languages and Automata Theory
2009-07-06 v1 Discrete Mathematics
Abstract
An infinite word is S-automatic if, for all n>=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>=2, we state that a multidimensional infinite word x : N^d \to \Sigma over a finite alphabet \Sigma is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word.
Keywords
Cite
@article{arxiv.0907.0615,
title = {Multidimensional Generalized Automatic Sequences and Shape-symmetric Morphic Words},
author = {Emilie Charlier and Tomi Karki and Michel Rigo},
journal= {arXiv preprint arXiv:0907.0615},
year = {2009}
}