Abstract
We give a survey of different possible generalizations of the notion of q-automatic sequences, then we focus on the concept of q- regular sequences, which was introduced by J. Shallit and the author in [3]. We finally give numerous examples of such sequences.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
references
J.-P. Allouche, Automates finis en théorie des nombres, Expo. Math. 5 (1987), 239–266.
J.-P. Allouche, Note sur un article de Sharif et Woodcock, Séminaire de Théorie des Nombres de Bordeaux, (Série 2) 1 (1989), 163–187.
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, to appear in Theor. Comp. Sci. (1991), see also Proceedings of STACS'90, Lecture Notes in Computer Science, 415, p. 12–23.
G. Christol, T. Kamae, M. Mendès France and G. Rauzy, Suites algébriques, automates et substitutions, Bull. Soc. Math. France 108 (1980), 401–419.
A. Cobham, Uniform tag sequences, Math. Systems Theory 6 (1972), 164–192.
F. M. Dekking, M. Mendès France and A. J. van der Poorten, FOLDS!, Math. Intell. 4 (1982), 130–138; 173–181; 190–195.
P. Deligne, Intégration sur un cycle évanescent, Invent. Math. 76 (1983), 129–143.
H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967), 271–277.
T. Harase, Algebraic elements in formal power series rings, Israel J. Math. 63, 3 (1988), 281–288.
L. Lipschitz and A. J. van der Poorten, Rational functions, diagonals, automata and arithmetic, in R. A. Mollin (ed.), First conference of the Canadian Number Theory Association, Banff/Can. (1988), (de Gruyter 1989).
C. Mauduit, Substitutions et ensembles normaux, Habilitation, Marseille, 1989.
O. Salon, Suitev automatiques à multi-indices, Séminaire de Théorie des Nombres de Bordeaux (1986–1987), 4-01–4-27, followed by an appendix of J. Shallit.
O. Salon, Suites automatiques à multi-indices et algébricité, C. R. Acad. Sci. Paris, Sér I t. 305 (1987), 501–504.
J. Shallit, A generalization of automatic sequences, Theor. Comp. Sci. 61 (1988), 1–16.
H. Sharif and C. F. Woodcock, Algebraic functions over a field of positive characteristic and Hadamard products, J. Lond. Math. Soc. (2) 37 (1988), 395–403.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973.
Z. X. Wen and Z. Y. Wen, Preprint.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Allouche, JP. (1992). q-Regular sequences and other generalizations of q-automatic sequences. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023813
Download citation
DOI: https://doi.org/10.1007/BFb0023813
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55284-0
Online ISBN: 978-3-540-47012-0
eBook Packages: Springer Book Archive