Radix enumeration of rational languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 19-36.

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.

DOI : 10.1051/ita/2010003
Classification : 68Q45, 68Q70
Mots-clés : finite automata, rational functions of words, sequential transducers 
@article{ITA_2010__44_1_19_0,
     author = {Angrand, Pierre-Yves and Sakarovitch, Jacques},
     title = {Radix enumeration of rational languages},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {19--36},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {1},
     year = {2010},
     doi = {10.1051/ita/2010003},
     mrnumber = {2604933},
     zbl = {1186.68243},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2010003/}
}
TY  - JOUR
AU  - Angrand, Pierre-Yves
AU  - Sakarovitch, Jacques
TI  - Radix enumeration of rational languages
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2010
SP  - 19
EP  - 36
VL  - 44
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita/2010003/
DO  - 10.1051/ita/2010003
LA  - en
ID  - ITA_2010__44_1_19_0
ER  - 
%0 Journal Article
%A Angrand, Pierre-Yves
%A Sakarovitch, Jacques
%T Radix enumeration of rational languages
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2010
%P 19-36
%V 44
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita/2010003/
%R 10.1051/ita/2010003
%G en
%F ITA_2010__44_1_19_0
Angrand, Pierre-Yves; Sakarovitch, Jacques. Radix enumeration of rational languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 19-36. doi : 10.1051/ita/2010003. http://www.numdam.org/articles/10.1051/ita/2010003/

[1] P.-Y. Angrand, J. Sakarovitch and R. De Souza, Sequential transducer cascades. In preparation.

[2] J. Berstel, Transductions and Context-Free Languages. Teubner (1979). | Zbl

[3] 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.

[4] V. Berthé, Ch. Frougny, M. Rigo and J. Sakarovitch, On the concrete complexity of the successor function. In preparation.

[5] Ch. Choffrut, Une caractérisation des fonctions séquentielles et des fonctions sous-séquentielles en tant que relations rationnelles. Theoret. Comput. Sci. 5 (1977) 325-337. | Zbl

[6] Ch. Choffrut and M.P. Schützenberger, Décomposition de fonctions rationnelles, Proc. STACS'86 , edited by B. Monien, G. Vidal-Naquet. Lect. Notes Comput. Sci. 210 (1986) 213-226. | Zbl

[7] S. Eilenberg, Automata, Languages and Machines, Vol. A, Academic Press (1974). | Zbl

[8] P. Lecomte and M. Rigo, Numeration systems on a regular language. Theor. Comput. Syst. 34 (2001) 27-44. | Zbl

[9] D. Perrin, Finite automata. Handbook of Theoretical Computer Science Vol. B, edited by J. van Leeuwen. Elsevier (1990) 1-53. | Zbl

[10] Ch. Reutenauer, 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. | Zbl

[11] J. Sakarovitch, Deux remarques sur un théorème de S. Eilenberg. RAIRO-Theor. Inf. Appl. 17 (1983) 23-48. | Numdam | Zbl

[12] J. Sakarovitch, Eléments de théorie des automates. Vuibert (2003). English corrected edition: Elements of Automata Theory, Cambridge University Press (2009). | Zbl

[13] M.P. Schützenberger, Sur une variante des fonctions séquentielles. Theoret. Comput. Sci. 4 (1977) 47-57. | Zbl

[14] J. Shallit, Numeration systems, linear recurrences, and regular sets. Inform. Comput. 113 (1994) 331-347. | Zbl

Cité par Sources :