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DOI: 10.4230/LIPIcs.FSCD.2021.19
URN: urn:nbn:de:0030-drops-142572
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14257/
Kim, Dohan ; Lynch, Christopher
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 |
