Tree Automata and Automata on Linear Orderings

Véronique Bruyère; Olivier Carton; Géraud Sénizergues

RAIRO - Theoretical Informatics and Applications (2009)

  • Volume: 43, Issue: 2, page 321-338
  • ISSN: 0988-3754

Abstract

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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].

How to cite

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Bruyère, Véronique, Carton, Olivier, and Sénizergues, Géraud. "Tree Automata and Automata on Linear Orderings." RAIRO - Theoretical Informatics and Applications 43.2 (2009): 321-338. <http://eudml.org/doc/250607>.

@article{Bruyère2009,
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]. },
author = {Bruyère, Véronique, Carton, Olivier, Sénizergues, Géraud},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Finite automata; words over linear orderings-trees; monadic second order logics.; finite automata; words over linear orderings; trees; monadic second-order logic},
language = {eng},
month = {4},
number = {2},
pages = {321-338},
publisher = {EDP Sciences},
title = {Tree Automata and Automata on Linear Orderings},
url = {http://eudml.org/doc/250607},
volume = {43},
year = {2009},
}

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
DA - 2009/4//
PB - EDP Sciences
VL - 43
IS - 2
SP - 321
EP - 338
AB - 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].
LA - eng
KW - Finite automata; words over linear orderings-trees; monadic second order logics.; finite automata; words over linear orderings; trees; monadic second-order logic
UR - http://eudml.org/doc/250607
ER -

References

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  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.  
  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.  
  3. V. Bruyère and O. Carton, Automata on linear orderings. J. Comput. System Sci.73 (2007) 1–24.  
  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.  
  5. B. Courcelle, Frontiers of infinite trees. RAIRO Theoretical Informatics12 (1978) 319–337.  
  6. F. Hausdorff, Grundzüge einer Theorie der geordneten Mengen. Math. Ann.65 (1908) 435–505.  
  7. S. Heilbrunner, An algorithm for the solution of fixed-point equations for infinite words. RAIRO Theoretical Informatics14 (1980) 131–141.  
  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).  
  9. M.O. Rabin, Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc.141 (1969) 1–35.  
  10. C. Rispal and O. Carton, Complementation of rational sets on countable scattered linear orderings. J. Found. Comput. Sci.16 (2005) 767–786.  
  11. J.G. Rosenstein, Linear Orderings. Academic Press, New York (1982).  
  12. W. Thomas, On frontiers of regular sets. RAIRO Theoretical Informatics20 (1986) 371–381.  

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