Logic and Rational Languages of Words Indexed by Linear Orderings

  • Nicolas Bedon
  • Alexis Bès
  • Olivier Carton
  • Chloé Rispal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


We prove that every rational language of words indexed by linear orderings is definable in monadic second-order logic. We also show that the converse is true for the class of languages indexed by countable scattered linear orderings, but false in the general case. As a corollary we prove that the inclusion problem for rational languages of words indexed by countable linear orderings is decidable.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nicolas Bedon
    • 1
  • Alexis Bès
    • 2
  • Olivier Carton
    • 3
  • Chloé Rispal
    • 1
  1. 1.Laboratoire d’informatique de l’Institut Gaspard Monge, CNRS UMR 8049Université Paris-Est and CNRS 
  2. 2.Université Paris-Est, LACL 
  3. 3.Université Paris 7 and CNRS, LIAFA, CNRS UMR 7089 

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