License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2012.313
URN: urn:nbn:de:0030-drops-38691
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3869/
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Lin, Anthony Widjaja

Accelerating tree-automatic relations

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Abstract

We study the problem of computing the transitive closure of tree-automatic (binary) relations, which are represented by tree automata. Such relations include classes of infinite systems generated by pushdown systems (PDS), ground tree rewrite systems (GTRS), PA-processes, and Turing machines, to name a few. Although this problem is unsolvable in general, we provide a semi-algorithm for the problem and prove completeness guarantee for PDS, GTRS, and PA-processes. The semi-algorithm is an extension of a known semi-algorithm for structure-preserving tree-automatic relations, for which completeness is guaranteed for several interesting parameterized systems over tree topology. Hence, there is a single generic procedure that solves reachability for PDS, GTRS, PA-processes, and several parameterized systems in a uniform way. As an application, we provide a single generic semi-algorithm for checking repeated reachability over tree-automatic relations, for which completeness is guaranteed for the aforementioned classes.

BibTeX - Entry

@InProceedings{lin:LIPIcs:2012:3869,
  author =	{Anthony Widjaja Lin},
  title =	{{Accelerating tree-automatic relations}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012) },
  pages =	{313--324},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{Deepak D'Souza and Telikepalli Kavitha and Jaikumar Radhakrishnan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2012/3869},
  URN =		{urn:nbn:de:0030-drops-38691},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.313},
  annote =	{Keywords: Semi-algorithm, Model Checking, Infinite Systems, Automata}
}

Keywords: Semi-algorithm, Model Checking, Infinite Systems, Automata
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Issue Date: 2012
Date of publication: 14.12.2012

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