automatic sequences; numeration system; regular language; complexity; substitution; morphic word
Abstract :
[en] Let L be an infinite regular language on a totally ordered alphabet (Σ,<). Feeding a finite deterministic automaton (with output) with the words of L, enumerated lexicographically with respect to <, leads to an infinite sequence over the output alphabet of the automaton. This process generalizes the concept of k-automatic sequence for abstract numeration systems on a regular language (instead of systems in base k). Here, we study the first properties of these sequences and their relations with numeration systems.
Disciplines :
Mathematics Computer science
Author, co-author :
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Generalization of automatic sequences for numeration systems on a regular language
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