Theoretical Computer Science
Handbook of formal languages, vol. 1
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
An Eilenberg Theorem for Words on Countable Ordinals
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Hierarchy Among Automata on Linear Orderings
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Ensembles reconnaissables de mots biinfinis
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
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In a preceding paper [V. Bruyère, O. Carton, Automata on linear orderings, in: J. Sgall, A. Pultr, P. Kolman (Eds.), MFCS'2001, in: Lect. Notes in Comput. Sci., vol. 2136, 2001, pp. 236-247. iGM report 2001-12], 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 show that deterministic automata do not have the same expressive power. Despite this negative result, we prove that rational sets of words of finite ranks are closed under complementation.