The Range and Roots Constraints: Specifying Counting and Occurrence Problems

We propose a simple declarative language for specifying a wide range of counting and occurrence constraints. This specification language is executable since it immediately provides a polynomial propagation algorithm. To illustrate the capabilities of this language, we specify a dozen global constraints taken from the literature. We observe one of three outcomes: we achieve generalized arc-consistency; we do not achieve generalized arc-consistency, but achieving generalized arcconsistency is NP-hard; we do not achieve generalized arc-consistency, but specialized propagation algorithms can do so in polynomial time. Experiments demonstrate that this specification language is both efficient and effective in practice.