NDLI: The Knuth-Bendix Completion Procedure and Thue Systems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Narendran, Paliath Kapur, Deepak
Copyright Year	1985
Abstract	The Knuth-Bendix completion procedure for term rewriting systems in many cases provides a decision procedure for equational theories and has been found to have many applications in various areas. We discuss the application of the Knuth-Bendix procedure to Thue systems. We use the notion of a reduced Thue system and show that for every Church-Rosser Thue system, there is a unique reduced Church-Rosser Thue system equivalent to it. Furthermore, the Knuth-Bendix completion procedure, when applied to a Thue system T, always produces the finite reduced Church-Rosser Thue system equivalent to T whenever such a system exists. Similar results can also be proved for almost-confluent Thue systems. Using properties of reduced Church-Rosser systems, we develop conditions under which a class of special Thue systems have equivalent finite Church-Rosser systems. In addition, we show that the completion procedure always terminates on finite parenthesized Thue systems, from which the termination of the completion procedure over ground-term-rewriting systems can be shown immediately. From the results discussed in this paper, we also obtain the termination of the Knuth-Bendix completion procedure for commutative Thue systems (commutative monoids) as a simple corollary.
Starting Page	1052
Ending Page	1072
Page Count	21
File Format	PDF
ISSN	00975397
DOI	10.1137/0214073
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	14
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	almost-confluent systems commutative monoids rewriting systems Thue systems ground terms Knuth-Bendix completion procedure Church-Rosser systems
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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