Journal of the ACM (JACM) - The MIT Press scientific computation series
A practical algorithm for exact array dependence analysis
Communications of the ACM
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
On implementing symmetry detection
Constraints
A novel approach for detecting symmetries in CSP models
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Detecting and breaking symmetries by reasoning on problem specifications
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Compositional derivation of symmetries for constraint satisfaction
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
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The presence of symmetries in a constraint satisfaction problem gives an opportunity for more efficient search. Within the class of matrix models, we show that the problem of deciding whether some well known permutations are model symmetries (solution symmetries on every instance) is undecidable. We then provide a new approach to proving the model symmetries 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 demonstrate this approach with an implementation that reduces equivalence to a sentence in Presburger arithmetic, using the modelling language MiniZinc and the term re-writing language Cadmium, and show that it is capable of proving common symmetries in models.