Numeration systems: a link between number theory and formal language theory

English

Rigo, Michel[Université de Liège - ULg > Département de mathématique > Mathématiques discrètes >]

28-Nov-2012

National

VUB/ULB Math. Colloquium

28-11-2012

Ph. Cara

Brussels

[en] Numeration systems ; Automata theory ; Formal langauges

[en] In this talk, we survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies about sets of integers whose base k expansions are recognized by some finite automaton. We do not expect any background from the audience, so we will present the basic definitions and many examples. We will not attempt to be exhaustive but try instead to present some actual research directions about numeration systems, recognizable sets of integers and automatic sequences. If there is enough time, we will brieﬂy sketch some results about transcendence related to the representation of real numbers.