The Search for Mal'cev Terms over Finite Quandles

The goal of this project is to identify Mal’cev terms over finite quandles, a subclass of right quasi- groups. Mal’cev terms are relevant in universal algebra because their existence imply tractability in a quandle, Q. One can instead, however, search for a binary Merling term, as a Merling term in Q exists if and only if a Mal’cev term exists in Q as well. This significantly speeds up the approach, as binary terms lend themselves to much simpler computation than ternary terms. This project achieves the stated goals by the use of a term rewriting system (TRS) evaluator, a normal form (NF) generator, and the program clausetester from LADR (Library for Automated Deduction Research) to generate Merling terms in Q. The program also contains a Mal’cev term generator used by the program finds to compute the associated Mal’cev term for each Mer- ling term. Overall, this project offers a flexible and simple way to determine the tractability of quandles.