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Logic and Rational Languages of Words Indexed by Linear Orderings

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Abstract

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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Authors and Affiliations

  1. Laboratoire d’informatique de l’Institut Gaspard Monge, Université Paris-Est and CNRS, Cité Descartes, 5, boulevard Descartes, Champs-sur-Marne, 77454, Marne-la-Vallee Cedex 2, France

    Nicolas Bedon & Chloé Rispal

  2. LACL, Université Paris XII-Val de Marne, 61, avenue du Général de Gaulle, 94010, Créteil Cedex, France

    Alexis Bès

  3. LIAFA, Université Paris 7 and CNRS, 75205, Paris Cedex 13, France

    Olivier Carton

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  1. Nicolas Bedon
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  2. Alexis Bès
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  3. Olivier Carton
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  4. Chloé Rispal
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Correspondence to Nicolas Bedon.

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Bedon, N., Bès, A., Carton, O. et al. Logic and Rational Languages of Words Indexed by Linear Orderings. Theory Comput Syst 46, 737–760 (2010). https://doi.org/10.1007/s00224-009-9222-6

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