Proving Symmetries by Model Transformation

  • Christopher Mears
  • Todd Niven
  • Marcel Jackson
  • Mark Wallace
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6876)


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.


Matrix Model Model Transformation Turing Machine Constraint Satisfaction Problem Model Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christopher Mears
    • 1
  • Todd Niven
    • 1
  • Marcel Jackson
    • 2
  • Mark Wallace
    • 1
  1. 1.Faculty of ITMonash UniversityAustralia
  2. 2.Department of MathematicsLa Trobe UniversityAustralia

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