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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.586
URN: urn:nbn:de:0030-drops-39672
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3967/
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Huschenbett, Martin

The Rank of Tree-Automatic Linear Orderings

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Abstract

A tree-automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. The finite condensation rank (FC-rank) of a linear ordering measures how far it is away from being dense. We prove that the FC-rank of every tree-automatic linear ordering is below omega^omega. This generalises Delhommé's result that each tree-automatic ordinal is less than omega^omega^omega. Furthermore, we show an analogue for tree-automatic linear orderings where the branching complexity of the trees involved is bounded.

BibTeX - Entry

@InProceedings{huschenbett:LIPIcs:2013:3967,
  author =	{Martin Huschenbett},
  title =	{{The Rank of Tree-Automatic Linear Orderings}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{586--597},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3967},
  URN =		{urn:nbn:de:0030-drops-39672},
  doi =		{10.4230/LIPIcs.STACS.2013.586},
  annote =	{Keywords: tree-automatic structures, linear orderings, finite condensation rank, computable model theory}
}

Keywords: tree-automatic structures, linear orderings, finite condensation rank, computable model theory
Collection: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 26.02.2013

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