Hausdorff rank of scattered context-free linear orders

Authors:
Zoltán Ésik;Szabolcs Iván
Affiliations:
Department of Informatics, University of Szeged, Szeged, Hungary;Department of Informatics, University of Szeged, Szeged, Hungary
Venue:
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Year:
2012

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Abstract

We consider context-free languages equipped with the lexicographic ordering. We show that when the lexicographic ordering of a context-free language is scattered, then its Hausdorff rank is less than ωω. As an application of this result, we obtain that an ordinal is the order type of the lexicographic ordering of a context-free language if and only if it is less than ωωω.