Automated reasoning and exhaustive search: Quasigroup existence problems (Q1343395)

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.