A simple algorithm for Mal'tsev constraints

A Mal'tsev operation is a ternary operation phi that satisfies the identities phi( x, y, y) = phi( y, y, x) = x. Constraint satisfaction problems involving constraints invariant under a Mal'tsev operation constitute an important class of constraint satisfaction problems, which includes the affine satisfiability problem, subgroup and near subgroup constraints, and many others. It is also known that any tractable case of the counting constraint satisfaction problem involves only Mal'tsev constraints. The first algorithm solving the arbitrary constraint satisfaction problem with Mal'tsev constraints has been given by Bulatov. However, this algorithm is very sophisticated and relies heavily on advanced algebraic machinery. In this paper, we give a different and much simpler algorithm for this type of constraint.