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Knuth-Bendix procedure and non deterministic behavior - an example

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Bibliographic Details
Title:	Knuth-Bendix procedure and non deterministic behavior - an example
Authors:	Gnaedig, I.
Publisher Information:	European Association for Theoretical Computer Science, Leiden
Subject Terms:	nondeterminism, rules ordering, Software, source code, etc. for problems pertaining to computer science, Knuth-Bendix algorithm, rewriting rules, completion, Theorem proving (deduction, resolution, etc.), rewriting systems
Description:	The author presents an example in order to illustrate the nondeterminism of the Knuth-Bendix algorithm, with respect to the ordering it uses. He introduces a set of rules describing the axioms of Boolean algebra, with an additional axiom, corresponding to a theorem to be refuted. The paper shows how different orderings on terms, during an execution of the Knuth- Bendix procedure on these rules, lead to different completion processes. It is also shown how eleven such different sessions produce only two different rewriting systems.
Document Type:	Article
File Description:	application/xml
Access URL:	https://zbmath.org/4080964
Accession Number:	edsair.c2b0b933574d..ef3d33876e1b3b02fbc442cda0bbd041
Database:	OpenAIRE

Description
Abstract:	The author presents an example in order to illustrate the nondeterminism of the Knuth-Bendix algorithm, with respect to the ordering it uses. He introduces a set of rules describing the axioms of Boolean algebra, with an additional axiom, corresponding to a theorem to be refuted. The paper shows how different orderings on terms, during an execution of the Knuth- Bendix procedure on these rules, lead to different completion processes. It is also shown how eleven such different sessions produce only two different rewriting systems.