Series-parallel languages on scattered and countable posets

Authors:
Nicolas Bedon;Chloé Rispal
Affiliations:
Université de Paris-Est, CNRS, Laboratoire d'informatique de l'Institut Gaspard Monge, UMR CNRS 8049, Marne-la-Vallée Cedex, France;Université de Paris-Est, CNRS, Laboratoire d'informatique de l'Institut Gaspard Monge, UMR CNRS 8049, Marne-la-Vallée Cedex, France
Venue:
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Year:
2007

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Abstract

We initiate a study on automata recognizing labelled posets constructed from scattered and countable linear orderings. More precisely, the class of labelled posets considered in this paper is the smallest containing letters, closed under finite parallel operation and sequential product indexed by all countable and scattered linear orderings. The first result of this paper establishes that those labelled posets are precisely the N-free ones. The second result is a Kleene-like theorem, which establishes that the class of languages of labelled posets accepted by branching automata is exactly the class of rational languages. This generalizes both the finite [9] and ?-labelled posets [2,6] cases, and the Kleene-like theorem on words on linear orderings [3].