Constraint Symmetries have been suggested as an appropriate subgroup of solution symmetries that can be more easily found than the complete group of symmetries. The concept is analyzed, and it becomes clear that a knowledge of the problem as deep as for finding the whole group is required to find that subset. Indeed, we show that the Microstructure Complement in most cases only finds a small fraction of the subgroup of Constraint Symmetries. Moreover, not all the symmetries it finds are truly Constraint Symmetries. We show also that in the context of point symmetries (as opposed to literal symmetries), the subgroup of Constraint Symmetries coincides with the whole solution symmetry group.


artificial intelligence, mathematical programming.

Author keywords

Symmetries, Constraint Satisfaction, Numerical Constraint Satisfaction, Symmetry Detection, Problem solving,

Scientific reference

P. Mestres and V. Ruiz de Angulo. Constraint symmetries. Technical Report IRI-TR-17-05, Institut de Robòtica i Informàtica Industrial, CSIC-UPC, 2017.