2026-07-22T13:14:13Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9176 2024-03-06T10:43:33Z ddc:004 open_access

Confluence of Prefix-Constrained Rewrite Systems Andrianarivelo, Nirina Réty, Pierre prefix-constrained term rewriting confluence critical pair Prefix-constrained rewriting is a strict extension of context-sensitive rewriting. We study the confluence of prefix-constrained rewrite systems, which are composed of rules of the form L: l -> r where L is a regular string language that defines the allowed rewritable positions. The usual notion of Knuth-Bendix's critical pair needs to be extended using regular string languages, and the convergence of all critical pairs is not enough to ensure local confluence. Thanks to an additional restriction we get local confluence, and then confluence for terminating systems, which makes the word problem decidable. Moreover we present an extended Knuth-Bendix completion procedure, to transform a non-confluent prefix-constrained rewrite system into a confluent one. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nirina Andrianarivelo and Pierre Réty 2018 Is Part Of LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2018.6 urn:nbn:de:0030-drops-91762 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.6 eng https://creativecommons.org/licenses/by/3.0/legalcode