6 papers
Real numbers having ultimately periodic representations in abstract numeration systems
P. Lecomte, M. Rigo
Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in cla…
Towards a characterization of the star-free sets of integers
Michel Rigo
Let U be a numeration system, a set X of integers is U-star-free if the set made up of the U-representations of the elements in X is a star-free regular language. Answering a quest…
Numeration systems on a regular language: Arithmetic operations, Recognizability and Formal power series
Michel Rigo
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a fin…
Construction of regular languages and recognizability of polynomials
Michel Rigo
A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinit…
Generalization of automatic sequences for numeration systems on a regular language
Michel Rigo
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically w…
Numeration systems on a regular language
Pierre B. A. Lecomte, Michel Rigo
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular languag…