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Documents authored by Gmeiner, Karl

Document
DOI: 10.4230/OASIcs.WPTE.2014.3
Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems

Authors: Karl Gmeiner and Naoki Nishida

Published in: OASIcs, Volume 40, First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (2014)

Abstract
Transforming conditional term rewrite systems (CTRSs) into unconditional systems (TRSs) is a common approach to analyze properties of CTRSs via the simpler framework of unconditional rewriting. In the past many different transformations have been introduced for this purpose. One class of transformations, so-called unravelings, have been analyzed extensively in the past. In this paper we provide an overview on another class of transformations that we call structure-preserving transformations. In these transformations the structure of the conditional rule, in particular their left-hand side is preserved in contrast to unravelings. We provide an overview of transformations of this type and define a new transformation that improves previous approaches.
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Karl Gmeiner and Naoki Nishida. Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems. In First International Workshop on Rewriting Techniques for Program Transformations and Evaluation. Open Access Series in Informatics (OASIcs), Volume 40, pp. 3-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{gmeiner_et_al:OASIcs.WPTE.2014.3,
  author =	{Gmeiner, Karl and Nishida, Naoki},
  title =	{{Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems}},
  booktitle =	{First International Workshop on Rewriting Techniques for Program Transformations and Evaluation},
  pages =	{3--14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-70-5},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{40},
  editor =	{Schmidt-Schau{\ss}, Manfred and Sakai, Masahiko and Sabel, David and Chiba, Yuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2014.3},
  URN =		{urn:nbn:de:0030-drops-45871},
  doi =		{10.4230/OASIcs.WPTE.2014.3},
  annote =	{Keywords: conditional term rewriting, unraveling, condition elimination}
}
Document
DOI: 10.4230/OASIcs.WPTE.2014.39
On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings

Authors: Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner

Published in: OASIcs, Volume 40, First International Workshop on Rewriting Techniques for Program Transformations and Evaluation (2014)

Abstract
In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is sound for weakly left-linear normal conditional term rewriting systems (CTRS). Here, soundness for a CTRS means that reduction of the transformed unconditional term rewriting system (TRS) creates no undesired reduction for the CTRS. We first show that every reduction sequence of the transformed TRS starting with a term corresponding to the one considered on the CTRS is simulated by the reduction of the TRS obtained by the simultaneous unraveling. Then, we use the fact that the unraveling is sound for weakly left-linear normal CTRSs.
Cite as

Naoki Nishida, Makishi Yanagisawa, and Karl Gmeiner. On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings. In First International Workshop on Rewriting Techniques for Program Transformations and Evaluation. Open Access Series in Informatics (OASIcs), Volume 40, pp. 39-50, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{nishida_et_al:OASIcs.WPTE.2014.39,
  author =	{Nishida, Naoki and Yanagisawa, Makishi and Gmeiner, Karl},
  title =	{{On Proving Soundness of the Computationally Equivalent Transformation for Normal Conditional Term Rewriting Systems by Using Unravelings}},
  booktitle =	{First International Workshop on Rewriting Techniques for Program Transformations and Evaluation},
  pages =	{39--50},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-70-5},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{40},
  editor =	{Schmidt-Schau{\ss}, Manfred and Sakai, Masahiko and Sabel, David and Chiba, Yuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.WPTE.2014.39},
  URN =		{urn:nbn:de:0030-drops-45850},
  doi =		{10.4230/OASIcs.WPTE.2014.39},
  annote =	{Keywords: conditional term rewriting, unraveling, condition elimination}
}
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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