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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.RTA.2011.139
URN: urn:nbn:de:0030-drops-31131
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3113/
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Bahr, Patrick

Modes of Convergence for Term Graph Rewriting

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Abstract

Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order resp. a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting. We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the resulting infinitary calculi of term graph rewriting exhibit the same correspondence as we know it from term rewriting: Convergence via the partial order is a conservative extension of the metric convergence.

BibTeX - Entry

@InProceedings{bahr:LIPIcs:2011:3113,
  author =	{Patrick Bahr},
  title =	{{Modes of Convergence for Term Graph Rewriting}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{139--154},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-30-9 },
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{10},
  editor =	{Manfred Schmidt-Schau{\ss}},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3113},
  URN =		{urn:nbn:de:0030-drops-31131},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.RTA.2011.139},
  annote =	{Keywords: term graphs, partial order, metric, infinitary rewriting, graph rewriting}
}

Keywords: term graphs, partial order, metric, infinitary rewriting, graph rewriting
Seminar: 22nd International Conference on Rewriting Techniques and Applications (RTA'11)
Issue Date: 2011
Date of publication: 26.04.2011


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