Proving Symmetries by Model Transformation

The presence of symmetries in a constraint satisfaction problem gives an opportunity for more efficient search. We provide a new way of proving the existence of solution symmetries in all instances of a class of matrix CSPs by way of model transformations. Given a model M and a candidate symmetry σ, the approach first syntactically applies σ to M and then shows that the resulting model σ(M) is semantically equivalent to M . We show an implementation of the method using the modelling language MiniZinc and the term re-writing language Cadmium and show that it is able to prove certain kinds of symmetry.