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Constraint-Based Multi-Completion Procedures for Term Rewriting Systems

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Please use this identifier to cite or link to this item:http://hdl.handle.net/2115/38897

Title: Constraint-Based Multi-Completion Procedures for Term Rewriting Systems
Authors: Sato, Haruhiko Browse this author →KAKEN DB
Kurihara, Masahito Browse this author →KAKEN DB
Winkler, Sarah Browse this author
Middeldorp, Aart Browse this author
Keywords: equational theorem proving
term rewriting system
Knuth-Bendix completion
multi-completion
constraint-based multi-completion
Issue Date: 1-Feb-2009
Publisher: IEICE - The Institute of Electronics, Information and Communication Engineers
Journal Title: IEICE Transactions on Information and Systems
Volume: E92-D
Issue: 2
Start Page: 220
End Page: 234
Publisher DOI: 10.1587/transinf.E92.D.220
Abstract: In equational theorem proving, convergent term rewriting systems play a crucial role. In order to compute convergent term rewriting systems, the standard completion procedure (KB) was proposed by Knuth and Bendix and has been improved in various ways. The multi-completion system MKB developed by Kurihara and Kondo accepts as input a set of reduction orders in addition to equations and efficiently simulates parallel processes each of which executes the KB procedure with one of the given orderings. Wehrman and Stump also developed a new variant of completion procedure, constraint-based completion, in which reduction orders need not be given by using automated modern termination checkers. As a result, the constraint-based procedures simulate the execution of parallel KB processes in a sequential way, but naive search algorithms sometimes cause serious inefficiency when the number of the potential reduction orders is large. In this paper, we present a new procedure, called a constraint-based multi-completion procedure MKBcs, by augmenting the constraint-based completion with the framework of the multi-completion for suppressing the combinatorial explosion by sharing inferences among the processes. The existing constraint-based system SLOTHROP, which basically employs the best-first search, is more efficient when its built-in heuristics for process selection are appropriate, but when they are not, our system is more efficient. Therefore, both systems have their role to play.
Rights: Copyright © 2009 The Institute of Electronics, Information and Communication Engineers
Relation: http://search.ieice.or.jp/
Type: article
URI: http://hdl.handle.net/2115/38897
Appears in Collections:情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 佐藤 晴彦

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