Automata on linear orderings

  • Authors:
  • Véronique Bruyère;Olivier Carton

  • Affiliations:
  • Institut d'Informatique, Université de Mons-Hainaut, Le Pentagone, 6 avenue du Champ de Mars, B-7000 Mons, Belgium;LIAFA, Université Paris 7, case 7014, 2 place Jussieu, F-75251 Paris cedex 05, France

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2007

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Abstract

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce finite automata and rational expressions for these words. We prove that for countable scattered linear orderings, these two notions are equivalent. This result extends Kleene's theorem.