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Published in:
2012 | OriginalPaper | Chapter
Hausdorff Rank of Scattered Context-Free Linear Orders
Authors : Zoltán Ésik, Szabolcs Iván
Published in: LATIN 2012: Theoretical Informatics
Publisher: Springer Berlin Heidelberg
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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
ω
ω
. 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
$\omega^{\omega^\omega}$
.