Abstract
Translating an arithmetical property of formal power series over a finite field into language theory, we obtain and extend results on symmetric differences of certain regular languages.
Keywords
- Finite Field
- Formal Power Series
- Regular Language
- Finite Automaton
- Language Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.-P. ALLOUCHE, M. MENDES FRANCE. Preprint.
J.-P. ALLOUCHE, M. MENDES FRANCE, A.J. van der POORTEN.-Indépendance algébrique de certaines séries formelles. Bull. Soc. Math. France, 116, 1988, 449–454.
G. CHRISTOL.-Fonctions et éléments algébriques, Pacific J. Math. 125, 1, 1986, 1–37.
G. CHRISTOL, T. KAMAE, M. MENDES FRANCE, G. RAUZY.-Suites algébriques, automates et substitutions, Bull. Soc. Math. France 108, 1980, 401–419.
J.-H. CONWAY.-Regular Algebra and Finite Machines, Chapmann and Hall, 1971.
S. EILENBERG.-Automata, Languages and Machines, vol. A, Academic Press, 1974.
T. HARASE.-Algebraic Elements in Formal Power Series Ring, Israël J. Math., 63, 3, 1988, 281–288.
M. MENDES FRANCE, A.J. van der POORTEN.-Automata and the arithmetic of formal power series, Acta Arith. 46, 1986, p. 211–214.
H. SHARIF, C.F. WOODCOCK.-Algebraic functions over a field of positive characteristic and Hadamard products, J. London Math. Soc. 37, 2, 1988, 395–403.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
Allouche, J.P., Flajolet, P., France, M.M. (1990). Algebraically independent formal power series: A language theory interpretation. In: Nagasaka, K., Fouvry, E. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 1434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097121
Download citation
DOI: https://doi.org/10.1007/BFb0097121
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52787-9
Online ISBN: 978-3-540-47147-9
eBook Packages: Springer Book Archive
