Abstract numeration systems; Bounded language; Multiplication by a constant
Abstract :
[en] Generalizations of positional number systems in which N is recognizable by finite automata are obtained by describing an arbitrary infinite regular language according to the genealogical ordering. More precisely, an abstract numeration system is a triple S = (L, Σ, <) where L is an infinite language over the totally ordered alphabet (Σ, <). Enumerating the elements of L genealogically with respect to < leads to a one-to-one map rS from N onto L. To any natural number n, it assigns the (n + 1)th word of L, its S-representation, while the inverse map valS sends any word belonging to L onto its numerical value. A subset X is said to be S-recognizable if rS (X) is a regular subset of L. We study the preservation of recognizability of a set of integers after multiplication by a
constant for abstract numeration systems built over a bounded language.
Disciplines :
Mathematics
Author, co-author :
Charlier, Emilie ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Structural properties of bounded languages with respect to multiplication by a constant