The Complexity of Global Constraints

International audienceWe study the computational complexity of reasoning with global constraints. We show that reasoning with such constraints is intractable in general. We then demonstrate how the same tools of computational com- plexity can be used in the design and analysis of spe- cific global constraints. In particular, we illustrate how computational complexity can be used to determine when a lesser level of local consistency should be en- forced, when decomposing constraints will lose prun- ing,andwhencombiningconstraintsistractable.We also show how the same tools can be used to study symmetry breaking, meta-constraints like the cardinal- ity constraint, and learning nogoods