Complementation of Rational Sets on Countable Scattered Linear Orderings

Abstract : In a preceding paper (Bruyère and Carton, automata on linear orderings, MFCS'01), automata have been introduced for words indexed by linear orderings. These automata are a generalization of automata for finite, infinite, bi-infinite and even transfinite words studied by Büchi. Kleene's theorem has been generalized to these words. We prove that rational sets of words on countable scattered linear orderings are closed under complementation using an algebraic approach.
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Chloé Rispal, Olivier Carton. Complementation of Rational Sets on Countable Scattered Linear Orderings. International Journal of Foundations of Computer Science, World Scientific Publishing, 2005, 16 (4), pp.767-786. ⟨hal-00160985⟩

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