General Algorithms for Permutations in Equational Inference

Mechanized systems for equational inference often produce many terms that are permutations of one another. We propose to gain efficiency by dealing with such sets of terms in a uniform manner, by the use of efficient general algorithms on permutation groups. We show how permutation groups arise natu...

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Bibliographic Details
Published inJournal of automated reasoning Vol. 26; no. 3; pp. 223 - 268
Main Authors Avenhaus, Jürgen, Plaisted, David A.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.04.2001
Subjects
Algorithms
Automated reasoning
Dealing
Gain
Inference
Permutations
Reasoning
Strategy
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ISSN0168-7433
1573-0670
DOI10.1023/A:1006439522342

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Summary:Mechanized systems for equational inference often produce many terms that are permutations of one another. We propose to gain efficiency by dealing with such sets of terms in a uniform manner, by the use of efficient general algorithms on permutation groups. We show how permutation groups arise naturally in equational inference problems, and study some of their properties. We also study some general algorithms for processing permutations and permutation groups, and consider their application to equational reasoning and term-rewriting systems. Finally, we show how these techniques can be incorproated into resolution theorem-proving strategies.[PUBLICATION ABSTRACT]
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ISSN:0168-7433
1573-0670
DOI:10.1023/A:1006439522342