no. 2
Tree automata and automata on linear orderings
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 321-338.

We show that the inclusion problem is decidable for rational languages of words indexed by scattered countable linear orderings. The method leans on a reduction to the decidability of the monadic second order theory of the infinite binary tree [9].

DOI : 10.1051/ita/2009009
Classification : 68Q45, 03D05
Mots clés : finite automata, words over linear orderings-trees, monadic second order logics 
@article{ITA_2009__43_2_321_0,
     author = {Bruy\`ere, V\'eronique and Carton, Olivier and S\'enizergues, G\'eraud},
     title = {Tree automata and automata on linear orderings},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {321--338},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {2},
     year = {2009},
     doi = {10.1051/ita/2009009},
     mrnumber = {2512262},
     zbl = {1166.68022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2009009/}
}
TY  - JOUR
AU  - Bruyère, Véronique
AU  - Carton, Olivier
AU  - Sénizergues, Géraud
TI  - Tree automata and automata on linear orderings
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2009
SP  - 321
EP  - 338
VL  - 43
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita/2009009/
DO  - 10.1051/ita/2009009
LA  - en
ID  - ITA_2009__43_2_321_0
ER  - 
%0 Journal Article
%A Bruyère, Véronique
%A Carton, Olivier
%A Sénizergues, Géraud
%T Tree automata and automata on linear orderings
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2009
%P 321-338
%V 43
%N 2
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita/2009009/
%R 10.1051/ita/2009009
%G en
%F ITA_2009__43_2_321_0
Bruyère, Véronique; Carton, Olivier; Sénizergues, Géraud. Tree automata and automata on linear orderings. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 321-338. doi : 10.1051/ita/2009009. http://www.numdam.org/articles/10.1051/ita/2009009/

[1] V. Bruyère and O. Carton, Automata on linear orderings, edited by J. Sgall, A. Pultr and P. Kolman, MFCS'2001. Lect. Notes Comput. Sci. 2136 (2001) 236-247. | MR | Zbl

[2] V. Bruyère, O. Carton and G. Sénizergues, Tree automata and automata on linear orderings, in Proceedings WORDS'03. Lect. Notes Comput. Sci. 27 (2003) 222-231. TUCS General Publication. | MR | Zbl

[3] V. Bruyère and O. Carton, Automata on linear orderings. J. Comput. System Sci. 73 (2007) 1-24. | MR | Zbl

[4] O. Carton, Accessibility in automata on scattered linear orderings, edited by K. Diks and W. Rytter, MFCS'2002. Lect. Notes Comput. Sci. 2420 (2002) 155-164. | MR | Zbl

[5] B. Courcelle, Frontiers of infinite trees. RAIRO Theoretical Informatics 12 (1978) 319-337. | Numdam | MR | Zbl

[6] F. Hausdorff, Grundzüge einer Theorie der geordneten Mengen. Math. Ann. 65 (1908) 435-505. | JFM | MR

[7] S. Heilbrunner, An algorithm for the solution of fixed-point equations for infinite words. RAIRO Theoretical Informatics 14 (1980) 131-141. | Numdam | MR | Zbl

[8] S.C. Kleene, Representation of events in nerve nets and finite automata, edited by C.E. Shannon, Automata studies, 3-41. Princeton University Press, Princeton (1956). | MR

[9] M.O. Rabin, Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc. 141 (1969) 1-35. | MR | Zbl

[10] C. Rispal and O. Carton, Complementation of rational sets on countable scattered linear orderings. J. Found. Comput. Sci. 16 (2005) 767-786. | MR | Zbl

[11] J.G. Rosenstein, Linear Orderings. Academic Press, New York (1982). | MR | Zbl

[12] W. Thomas, On frontiers of regular sets. RAIRO Theoretical Informatics 20 (1986) 371-381. | Numdam | MR | Zbl

Cité par Sources :