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URN: urn:nbn:de:0030-drops-142572
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An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems

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Abstract

Rewriting modulo equations has been researched for several decades but due to the lack of suitable orderings, there are some limitations to rewriting modulo permutation equations. Given a finite set of permutation equations E, we present a new RPO-based ordering modulo E using (permutation) group actions and their associated orbits. It is an E-compatible reduction ordering on terms with the subterm property and is E-total on ground terms. We also present a completion and ground completion method for rewriting modulo a finite set of permutation equations E using our ordering modulo E. We show that our ground completion modulo E always admits a finite ground convergent (modulo E) rewrite system, which allows us to obtain the decidability of the word problem of ground theories modulo E.

BibTeX - Entry

@InProceedings{kim_et_al:LIPIcs.FSCD.2021.19,
  author =	{Kim, Dohan and Lynch, Christopher},
  title =	{{An RPO-Based Ordering Modulo Permutation Equations and Its Applications to Rewrite Systems}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14257},
  URN =		{urn:nbn:de:0030-drops-142572},
  doi =		{10.4230/LIPIcs.FSCD.2021.19},
  annote =	{Keywords: Recursive Path Ordering, Permutation Equation, Permutation Group, Rewrite System, Completion, Ground Completion}
}

Keywords: Recursive Path Ordering, Permutation Equation, Permutation Group, Rewrite System, Completion, Ground Completion
Seminar: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)
Issue date: 2021
Date of publication: 06.07.2021


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