A Kleene Theorem for Languages of Words Indexed by Linear Orderings

Abstract : In a preceding paper, Bruyère and Carton introduced automata, as well as rational expressions, which allow to deal with words indexed by linear orderings. A Kleene-like theorem was proved for words indexed by countable scattered linear orderings. In this paper we extend this result to languages of words indexed by all linear orderings.
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Alexis Bès, Olivier Carton. A Kleene Theorem for Languages of Words Indexed by Linear Orderings. International Journal of Foundations of Computer Science, World Scientific Publishing, 2006, 17 (3), pp.519-542. ⟨hal-00160976⟩

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