1. Multidimensional Generalized Automatic Sequences and Shape-symmetric Morphic Words
- Author
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Michel Rigo, Tomi Kärki, and Emilie Charlier
- Subjects
FOS: Computer and information sciences ,Discrete Mathematics (cs.DM) ,Formal Languages and Automata Theory (cs.FL) ,Computer Science - Formal Languages and Automata Theory ,Theoretical Computer Science ,Combinatorics ,Morphism ,Morphic word ,Regular language ,Deterministic automaton ,Automatic sequence ,Discrete Mathematics and Combinatorics ,Mathematics ,Discrete mathematics ,Multidimensional word ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,Abstract numeration system ,Shape-symmetry ,Automaton ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,If and only if ,Computer Science::Formal Languages and Automata Theory ,Computer Science - Discrete Mathematics ,Coding (social sciences) - 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.
- Published
- 2009
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