Representing real numbers in a generalized numeration system

Authors:
ímilie Charlier;Marion Le Gonidec;Michel Rigo
Affiliations:
Institut de Mathématiques, Université de Liège, Grande Traverse 12 (B 37), B-4000 Liège, Belgium;Laboratoire IMATH, Université de Toulon, Avenue de luniversité - BP 20132, 83957 La Garde Cedex, France;Institut de Mathématiques, Université de Liège, Grande Traverse 12 (B 37), B-4000 Liège, Belgium
Venue:
Journal of Computer and System Sciences
Year:
2011

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Abstract

We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show that our framework can be applied to the rational base numeration systems.