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Multi-Completion with Termination Tools

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Title: Multi-Completion with Termination Tools
Authors: Winkler, Sarah Browse this author
Sato, Haruhiko Browse this author →KAKEN DB
Middeldorp, Aart Browse this author
Kurihara, Masahito Browse this author →KAKEN DB
Keywords: Term rewriting
Knuth-Bendix completion
Termination tools
Issue Date: Mar-2013
Publisher: Springer Netherlands
Journal Title: Journal of Automated Reasoning
Volume: 50
Issue: 3
Start Page: 317
End Page: 354
Publisher DOI: 10.1007/s10817-012-9249-2
Abstract: Knuth-Bendix completion is a classical calculus in automated deduction for transforming a set of equations into a confluent and terminating set of directed equations which can be used to decide the induced equational theory. Multi-completion with termination tools constitutes an approach that differs from the classical method in two respects: (1) external termination tools replace the reduction order-a typically critical parameter-as proposed by Wehrman et al. (2006), and (2) multi-completion as introduced by Kurihara and Kondo (1999) is used to keep track of multiple orientations in parallel while exploiting sharing to boost efficiency. In this paper we describe the inference system, give the full proof of its correctness and comment on completeness issues. Critical pair criteria and isomorphisms are presented as refinements together with all proofs. We furthermore describe the implementation of our approach in the tool mkbTT, present extensive experimental results and report on new completions.
Type: article
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: 栗原 正仁

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