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.
|Number of pages||21|
|Journal||Commentationes Mathematicae Universitatis Carolinae|
|Publication status||Published - 2008|
- Automated reasoning