Proving Symmetries by Model Transformation

  • Christopher Mears
  • Todd Niven
  • Marcel Jackson
  • Mark Wallace
Conference paper

DOI: 10.1007/978-3-642-23786-7_45

Volume 6876 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Mears C., Niven T., Jackson M., Wallace M. (2011) Proving Symmetries by Model Transformation. In: Lee J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg

Abstract

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.

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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