Hierarchy among Automata on Linear Orderings

Véronique Bruyère (1) , Olivier Carton (2)

1 Institute of Computer Science [Mons]
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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.

Domaines: Algorithme et structure de données [cs.DS]

Véronique Bruyère, Olivier Carton. Hierarchy among Automata on Linear Orderings. Theory of Computing Systems, 2005, 38 (5), pp.593-621. ⟨hal-00161039⟩