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 ordering are closed under complementation using an algebraic approach.
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Rispal, C., Carton, O. (2004). Complementation of Rational Sets on Countable Scattered Linear Orderings. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_32
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DOI: https://doi.org/10.1007/978-3-540-30550-7_32
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