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Classification results in quasigroup and loop theory via a combination of automated reasoning tools
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 319-339 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 20N05, 68T15, 68W30, 81T05
Keywords: quasigroups; loops; classification; automated reasoning 
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     title = {Classification results in quasigroup and loop theory via a combination of automated reasoning tools},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {319--339},
     year = {2008},
     volume = {49},
     number = {2},
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     zbl = {1192.20062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_2_a13/}
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Sorge, Volker; Colton, Simon; McCasland, Roy; Meier, Andreas. Classification results in quasigroup and loop theory via a combination of automated reasoning tools. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 319-339. http://geodesic.mathdoc.fr/item/CMUC_2008_49_2_a13/