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Documents authored by Gramlich, Bernhard

Document
DOI: 10.4230/LIPIcs.RTA.2012.193
On Soundness Conditions for Unraveling Deterministic Conditional Rewrite Systems

Authors: Karl Gmeiner, Bernhard Gramlich, and Felix Schernhammer

Published in: LIPIcs, Volume 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12) (2012)

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.
Cite as

Karl Gmeiner, Bernhard Gramlich, and Felix Schernhammer. On Soundness Conditions for Unraveling Deterministic Conditional Rewrite Systems. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 193-208, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{gmeiner_et_al:LIPIcs.RTA.2012.193,
  author =	{Gmeiner, Karl and Gramlich, Bernhard and Schernhammer, Felix},
  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 =	{Tiwari, Ashish},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2012.193},
  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}
}
Document
DOI: 10.4230/LIPIcs.RTA.2010.119
On (Un)Soundness of Unravelings

Authors: Karl Gmeiner, Bernhard Gramlich, and Felix Schernhammer

Published in: LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010)

Abstract
We revisit (un)soundness of transformations of conditional into unconditional rewrite systems. The focus here is on so-called unravelings, the most simple and natural kind of such transformations, for the class of normal conditional systems without extra variables. By a systematic and thorough study of existing counterexamples and of the potential sources of unsoundness we obtain several new positive and negative results. In particular, we prove the following new results: Confluence, non-erasingness and weak left-linearity (of a given conditional system) each guarantee soundness of the unraveled version w.r.t. the original one. The latter result substantially extends the only known sufficient criterion for soundness, namely left-linearity. Furthermore, by means of counterexamples we refute various other tempting conjectures about sufficient conditions for soundness.
Cite as

Karl Gmeiner, Bernhard Gramlich, and Felix Schernhammer. On (Un)Soundness of Unravelings. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 119-134, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{gmeiner_et_al:LIPIcs.RTA.2010.119,
  author =	{Gmeiner, Karl and Gramlich, Bernhard and Schernhammer, Felix},
  title =	{{On (Un)Soundness of Unravelings}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{119--134},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Lynch, Christopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.119},
  URN =		{urn:nbn:de:0030-drops-26485},
  doi =		{10.4230/LIPIcs.RTA.2010.119},
  annote =	{Keywords: Conditional rewriting, transformation into unconditional systems, unsoundness, unraveling}
}
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