About frequencies of letters in generalized automatic sequences

[en] We present some asymptotic results about the frequency of a letter appearing in a generalized unidimensional automatic sequence. Next, we study multidimensional generalized automatic sequences and the corresponding frequencies. (C) 2006 Elsevier B.V. All rights reserved.

Disciplines :

Mathematics
Computer science

Author, co-author :

Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse, analyse fonctionnelle, ondelettes

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

Language :

English

Title :

About frequencies of letters in generalized automatic sequences

Publication date :

20 April 2007

Journal title :

Theoretical Computer Science

ISSN :

0304-3975

Publisher :

Elsevier Science, Amsterdam, Netherlands

Volume :

374

Issue :

1-3

Pages :

25-40

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 01 July 2009

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Bibliography

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Grabner P.J., and Rigo M. Additive functions with respect to numeration systems on regular languages. Monatsh. Math. 139 (2003) 205-219
Lecomte P., and Rigo M. Numeration systems on a regular language. Theory Comput. Syst. 34 (2001) 27-44
Lecomte P., and Rigo M. On the representation of real numbers using regular languages. Theory Comput. Syst. 35 (2002) 13-38
Lind D., and Marcus B. An Introduction to Symbolic Dynamics and Coding (1995), Cambridge University Press, Cambridge
Peter M. The asymptotic distribution of elements in automatic sequences. Theoret. Comput. Sci. 301 (2003) 285-312
Peyrière J. Fréquence des motifs dans les suites doubles invariantes par une substitution. Ann. Sci. Math. Québec 11 (1987) 133-138
Rigo M. Generalization of automatic sequences for numeration systems on a regular language. Theoret. Comput. Sci. 244 (2000) 271-281
Rigo M., and Maes A. More on generalized automatic sequences. J. Autom. Lang. Comb. 7 (2002) 351-376
Saari K. On the frequency of letters in pure binary morphic sequences. Developments in Language Theory. Lect. Notes Comput. Sci. vol. 3572 (2005), Springer 397-408
O. Salon, Suites automatiques à multi-indices, in: Séminaire de théorie des nombres de Bordeaux, Exp. 4 (1986-1987), 4.01-4.27. Followed by an Appendix by J. Shallit, 4-29A-4-36A
Yablonski S. Introduction aux mathématiques discrètes (1983), Mir, Moscow

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