License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.RTA.2012.193
URN: urn:nbn:de:0030-drops-34936
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3493/
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Gmeiner, Karl ; Gramlich, Bernhard ; Schernhammer, Felix

On Soundness Conditions for Unraveling Deterministic Conditional Rewrite Systems

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Abstract

We study (un)soundness of transformations of conditional term rewriting systems (CTRSs) into unconditional term rewriting systems (TRSs). The focus here is on analyzing (un)soundness of so-called unravelings, the most basic and natural class of such transformations. We extend our previous analysis from normal 1-CTRSs to the more general class of deterministic CTRSs (DCTRSs) where extra variables in right-hand sides of rules are allowed to a certain extent. We prove that the previous soundness results based on weak left-linearity and on right-linearity can be extended from normal 1-CTRSs to DCTRSs. Counterexamples show that such an extension to DCTRSs does not work for the previous criteria which were based on confluence and on non-erasingness, not even for right-stable systems. Yet, we prove weaker versions of soundness criteria based on confluence and on non-erasingness. Finally, we compare our approach and results with other recently established soundness criteria for unraveling DCTRSs.

BibTeX - Entry

@InProceedings{gmeiner_et_al:LIPIcs:2012:3493,
  author =	{Karl Gmeiner and Bernhard Gramlich and Felix Schernhammer},
  title =	{{On Soundness Conditions for Unraveling Deterministic Conditional Rewrite Systems}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12) },
  pages =	{193--208},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-38-5},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{15},
  editor =	{Ashish Tiwari},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3493},
  URN =		{urn:nbn:de:0030-drops-34936},
  doi =		{10.4230/LIPIcs.RTA.2012.193},
  annote =	{Keywords: Conditional term rewriting system (CTRS), deterministic   CTRS, transformation, simulation, soundness}
}

Keywords: Conditional term rewriting system (CTRS), deterministic CTRS, transformation, simulation, soundness
Collection: 23rd International Conference on Rewriting Techniques and Applications (RTA'12)
Issue Date: 2012
Date of publication: 29.05.2012

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