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Tree Automata and Automata on Linear Orderings

Published online by Cambridge University Press:  03 April 2009

Véronique Bruyère
Affiliation:
Université de Mons-Hainaut, France; Veronique.Bruyere@umh.ac.be
Olivier Carton
Affiliation:
LIAFA, Université Paris 7, France; Olivier.Carton@liafa.jussieu.fr
Géraud Sénizergues
Affiliation:
LaBRI, Université de Bordeaux I, France; ges@labri.u-bordeaux.fr
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Abstract

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].

Type
Research Article
Copyright
© EDP Sciences, 2008

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References

Bruyère, V. and Carton, O., Automata on linear orderings, edited by J. Sgall, A. Pultr and P. Kolman, MFCS'2001. Lect. Notes Comput. Sci. 2136 (2001) 236247. CrossRef
Bruyère, V., Carton, O. and Sénizergues, G., Tree automata and automata on linear orderings, in Proceedings WORDS'03. Lect. Notes Comput. Sci. 27 (2003) 222231. TUCS General Publication.
Bruyère, V. and Carton, O., Automata on linear orderings. J. Comput. System Sci. 73 (2007) 124. CrossRef
Carton, O., Accessibility in automata on scattered linear orderings, edited by K. Diks and W. Rytter, MFCS'2002. Lect. Notes Comput. Sci. 2420 (2002) 155164. CrossRef
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Hausdorff, F., Grundzüge einer Theorie der geordneten Mengen. Math. Ann. 65 (1908) 435505. CrossRef
Heilbrunner, S., An algorithm for the solution of fixed-point equations for infinite words. RAIRO Theoretical Informatics 14 (1980) 131141. CrossRef
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).
Rabin, M.O., Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc. 141 (1969) 135.
Rispal, C. and Carton, O., Complementation of rational sets on countable scattered linear orderings. J. Found. Comput. Sci. 16 (2005) 767786. CrossRef
J.G. Rosenstein, Linear Orderings. Academic Press, New York (1982).
Thomas, W., On frontiers of regular sets. RAIRO Theoretical Informatics 20 (1986) 371381. CrossRef

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