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Classification results in quasigroup and loop theory via a combination of automated reasoning tools

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Original languageEnglish
Pages (from-to)319-339
Number of pages21
JournalCommentationes Mathematicae Universitatis Carolinae
Volume49
Issue number2
Publication statusPublished - 2008

Abstract

We present some novel classification results in quasigroup and loop theory. For quasigroups up to size 5 and loops up to size 7, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques --- including machine learning and computer algebra --- which we present here. Moreover, each result has been automatically verified, again using a variety of techniques --- including automated theorem proving, computer algebra and satisfiability solving --- and we describe our bootstrapping approach to the generation and verification of these classification results.

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