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.
CITATION STYLE
Bruyère, V., & Carton, O. (2002). Hierarchy among automata on linear orderings. IFIP Advances in Information and Communication Technology, 96, 107–118. https://doi.org/10.1007/978-0-387-35608-2_10
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