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Hierarchy Among Automata on Linear Orderings

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Abstract

In a preceding paper, automata and rational expressions have been introduced for words indexed by linear orderings, together with a Kleene-like theorem. We here pursue this work by proposing a hierarchy among the rational sets. Each class of the hierarchy is defined by a subset of the rational operations that can be used. We then characterize any class by an appropriate class of automata, leading to a Kleene theorem inside the class. A characterization by particular classes of orderings is also given.

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Authors and Affiliations

  1. Institut d’Informatique, Universite de Mons-Hainaut, Le Pentagone, 6 avenue du Champ de Mars, B-7000 Mons, Belgium

    Véronique Bruyére

  2. LIAFA, Universite Paris 7, 5 place Jussieu, F-75251 Paris Cedex 05, France

    Olivier Carton

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  1. Véronique Bruyére
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  2. Olivier Carton
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Correspondence to Véronique Bruyére or Olivier Carton.

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Bruyére, V., Carton, O. Hierarchy Among Automata on Linear Orderings. Theory Comput Syst 38, 593–621 (2005). https://doi.org/10.1007/s00224-005-1129-2

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  • DOI: https://doi.org/10.1007/s00224-005-1129-2

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