Numeration systems; Cobham's theorem; automatic sequence; Number theory
Abstract :
[en] Considering an integer base b, any integer is represented by a word over a finite digit-set, its base-b expansion. In theoretical computer science, one is interested in syntactical properties of words or languages, i.e., sets of words. In this introductory talk, I will present recognizable sets of numbers : the set of their representations is accepted by a finite automaton. We will see that this property strongly depends on the choice of the numeration system. We will therefore review some fundamental questions and introduce automatic sequences. Thanks to Büchi-Bruyère theorem, first order logic and decidable theories may be used to produce automatic proofs and in particular solve, in an automated way, arithmetical problems. I will not assume any knowledge from the audience about formal languages theory.
Disciplines :
Mathematics
Author, co-author :
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Numeration systems: a bridge between formal languages and number theory
Publication date :
2022
Event name :
Arithmétique en Plat Pays
Event organizer :
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville