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DOI: 10.4230/LIPIcs.FSTTCS.2021.44

Confluence of Conditional Rewriting in Logic Form

Authors: Raúl Gutiérrez, Salvador Lucas, and Miguel Vítores

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract

We characterize conditional rewriting as satisfiability in a Herbrand-like model of terms where variables are also included as fresh constant symbols extending the original signature. Confluence of conditional rewriting and joinability of conditional critical pairs is characterized similarly. Joinability of critical pairs is then translated into combinations of (in)feasibility problems which can be efficiently handled by a number of automatic tools. This permits a more efficient use of standard results for proving confluence of conditional term rewriting systems, most of them relying on auxiliary proofs of joinability of conditional critical pairs, perhaps with additional syntactical and (operational) termination requirements on the system. Our approach has been implemented in a new system: CONFident . Its ability to (dis)prove confluence of conditional term rewriting systems is witnessed by means of some benchmarks comparing our tool with existing tools for similar purposes.

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Raúl Gutiérrez, Salvador Lucas, and Miguel Vítores. Confluence of Conditional Rewriting in Logic Form. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gutierrez_et_al:LIPIcs.FSTTCS.2021.44,
  author =	{Guti\'{e}rrez, Ra\'{u}l and Lucas, Salvador and V{\'\i}tores, Miguel},
  title =	{{Confluence of Conditional Rewriting in Logic Form}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{44:1--44:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.44},
  URN =		{urn:nbn:de:0030-drops-155553},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.44},
  annote =	{Keywords: Confluence, Program analysis, Rewriting-based systems}
}

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Confluence of Conditional Rewriting in Logic Form

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