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Radix enumeration of rational languages

Published online by Cambridge University Press:  11 February 2010

Pierre-Yves Angrand  and
Jacques Sakarovitch
Pierre-Yves Angrand
Affiliation:
LTCI (UMR 5141), Telecom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France; angrand@enst.fr
Jacques Sakarovitch
Affiliation:
LTCI (UMR 5141), CNRS / Telecom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France; sakarovitch@enst.fr
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Abstract

We prove that the function that maps a word of a rational language onto its successor for the radix order in this language is a finite union of co-sequential functions.

Keywords

Finite automatarational functions of wordssequential transducers.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 1: Special issue dedicated to the 12th "Journées Montoises d'Informatique Théorique" , January 2010 , pp. 19 - 36
Copyright
© EDP Sciences, 2010

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References

P.-Y. Angrand, J. Sakarovitch and R. de Souza, Sequential transducer cascades. In preparation.
J. Berstel, Transductions and Context-Free Languages. Teubner (1979).
V. Berthé, Ch. Frougny, M. Rigo and J. Sakarovitch, On the cost and complexity of the successor function, in Proc. WORDS 2007, edited by P. Arnoux, N. Bédaride and J. Cassaigne, Tech. Rep., Institut de mathématiques de Luminy (Marseille) (2007) 43–56.
V. Berthé, Ch. Frougny, M. Rigo and J. Sakarovitch, On the concrete complexity of the successor function. In preparation.
Choffrut, Ch., Une caractérisation des fonctions séquentielles et des fonctions sous-séquentielles en tant que relations rationnelles. Theoret. Comput. Sci. 5 (1977) 325–337. CrossRef
Choffrut, Ch. and Schützenberger, M.P., Décomposition de fonctions rationnelles, Proc. STACS'86 , edited by B. Monien, G. Vidal-Naquet. Lect. Notes Comput. Sci. 210 (1986) 213–226. CrossRef
S. Eilenberg, Automata, Languages and Machines, Vol. A, Academic Press (1974).
Lecomte, P. and Rigo, M., Numeration systems on a regular language. Theor. Comput. Syst. 34 (2001) 27–44. CrossRef
D. Perrin, Finite automata. Handbook of Theoretical Computer Science Vol. B, edited by J. van Leeuwen. Elsevier (1990) 1–53.
Reutenauer, Ch., Une caractérisation de la finitude de l'ensemble des coefficients d'une série rationnelle en plusieurs variables non commutatives. C. R. Acad. Sci. Paris 284 (1977) 1159–1162.
Sakarovitch, J., Deux remarques sur un théorème de S. Eilenberg. RAIRO-Theor. Inf. Appl. 17 (1983) 23–48.
J. Sakarovitch, Eléments de théorie des automates. Vuibert (2003). English corrected edition: Elements of Automata Theory, Cambridge University Press (2009).
Schützenberger, M.P., Sur une variante des fonctions séquentielles. Theoret. Comput. Sci. 4 (1977) 47–57. CrossRef
Shallit, J., Numeration systems, linear recurrences, and regular sets. Inform. Comput. 113 (1994) 331–347. CrossRef