Representing real numbers in a generalized numeration system

Charlier, Emilie; Le Gonidec, Marion; Rigo, Michel

doi:10.1016/j.jcss.2010.07.002

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Article (Scientific journals)

Representing real numbers in a generalized numeration system

Charlier, Emilie; Le Gonidec, Marion; Rigo, Michel

2011 • In Journal of Computer and System Sciences, 77, p. 743-759

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/38527

DOI
10.1016/j.jcss.2010.07.002

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Keywords :

real numbers; representation; numeration system; dyck language; infinite word; rational base

Abstract :

[en] 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.

Disciplines :

Computer science
Mathematics

Author, co-author :

Charlier, Emilie ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Le Gonidec, Marion

Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes

Language :

English

Title :

Representing real numbers in a generalized numeration system

Publication date :

2011

Journal title :

Journal of Computer and System Sciences

ISSN :

0022-0000

eISSN :

1090-2724

Publisher :

Academic Press

Volume :

Pages :

743-759

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 22 May 2010

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3 (3 by ULiège)

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Bibliography

Akiyama, S., Frougny, C., Sakarovitch, J., Powers of rationals modulo 1 and rational base number systems (2008) Israel J. Math., 168, pp. 53-91
Berstel, J., Boasson, L., The Set of Minimal Words of a Context-free Language is Context-free (1997) Journal of Computer and System Sciences, 55 (3), pp. 477-488
Boasson, L., Nivat, M., Adherences of languages (1980) J. Comput. System Sci., 20 (3), pp. 285-309
Bourbaki, N., (2007) Fonctions D Une Variable Réelle, , Springer Berlin, Heidelberg
Dumont, J.-M., Thomas, A., Systèmes de numération et fonctions fractales relatifs aux substitutions (1989) Theoret. Comput. Sci., 65 (2), pp. 153-169
Eilenberg, S., Automata, Languages, and Machines, vol. A (1974) Pure Appl. Math., 58. , Academic Press New York
Graham, R.L., Knuth, D.E., Patashnik, O., (1994) Concrete Mathematics: A Foundation for Computer Science, , second edition Addison-Wesley Publishing Company Reading, MA
Halbeisen, L., Hungerbühler, N., The Josephus problem (1997) J. Theor. Nombres Bordeaux, 9 (2), pp. 303-318
Le Gonidec, M., On complexity of infinite words associated with generalized Dyck languages (2008) Theoret. Comput. Sci., 407 (13), pp. 117-133
Lothaire, M., Algebraic Combinatorics on Words (2002) Encyclopedia Math. Appl., 90. , Cambridge University Press Cambridge
Lecomte, P.B.A., Rigo, M., Numeration systems on a regular language (2001) Theory Comput. Syst., 34 (1), pp. 27-44
Lecomte, P., Rigo, M., On the representation of real numbers using regular languages (2002) Theory of Computing Systems, 35 (1), pp. 13-38
Lecomte, P., Rigo, M., Real numbers having ultimately periodic representations in abstract numeration systems (2004) Inform. and Comput., 192, pp. 57-83
Nivat Maurice, Groups of Infinite Words Generated by an Algebraic Grammar (1978) RAIRO Inf Theor Theor Comput Sci, 12 (3), pp. 259-278
Odlyzko, A., Wilf, H., Functional iteration and the Josephus problem (1991) Glasg. Math. J., 33 (2), pp. 235-240
Sakarovitch, J., (2003) Élements de Théorie des Automates, , Vuibert Paris
Stephan, R., (2003) On A Sequence Related to the Josephus Problem, , http://arxiv.org/abs/math/0305348v1
Szilard, A., Yu, S., Zhang, K., Shallit, J., Characterizing regular languages with polynomial densities (1992) Lecture Notes in Comput. Sci., 629, pp. 494-503. , Springer Berlin Mathematical Foundations of Computer Science 1992 Prague, 1992