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DOI: 10.4230/LIPIcs.FSTTCS.2011.276
URN: urn:nbn:de:0030-drops-33220
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3322/
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Göller, Stefan ; Lohrey, Markus

The First-Order Theory of Ground Tree Rewrite Graphs

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Abstract

We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.

BibTeX - Entry

@InProceedings{gller_et_al:LIPIcs:2011:3322,
  author =	{Stefan G{\"o}ller and Markus Lohrey},
  title =	{{The First-Order Theory of Ground Tree Rewrite Graphs}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{276--287},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Supratik Chakraborty and Amit Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3322},
  URN =		{urn:nbn:de:0030-drops-33220},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2011.276},
  annote =	{Keywords: ground tree rewriting systems, first-order theories, complexity}
}

Keywords: ground tree rewriting systems, first-order theories, complexity
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)
Issue Date: 2011
Date of publication: 01.12.2011


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