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Slaney, J.; Fujita, M.; Stickel, Mark E.

Automated reasoning and exhaustive search: Quasigroup existence problems. (English) Zbl 0827.20083

Comput. Math. Appl. 29, No. 2, 115-132 (1995).
The authors investigate the existence of some finite quasigroups using three different automated reasoning programs: DDPP, FINDER and MGTP. Their attention is concentrated on some \((i,j,k)\)-conjugate orthogonal idempotent Latin squares of order \(v\) (COILS(\(v\))) and quasigroups satisfying one of the identities: \(ab.ba=a\), \(ab.ba=b\), \((ba.b)b=a\), \(ab.b=a.ab\), \(a.ba=ba.b\), where the order is some \(v \geq 8\). The existence or nonexistence is proved by experimental evidence. The computations of such hard problems are very complicated. The programs DDPP, FINDER and MGTP are described, and in several cases the authors give their search times for comparison.
Reviewer: E.Brožíková (Praha)

Cited in 14 Documents

MSC:

20N05 Loops, quasigroups
20-04 Software, source code, etc. for problems pertaining to group theory
05B15 Orthogonal arrays, Latin squares, Room squares
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
68W30 Symbolic computation and algebraic computation

Keywords:

finite quasigroups; automated reasoning programs; orthogonal idempotent Latin squares; identities

Software:

FINDER
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Full Text: DOI

References:

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