Résumé
We introduce some new mappings of constraint satisfaction problems into propositional satisfiability. These encodings generalize most of the existing encodings. Unit propagation on those encodings is the same as establishing relational k-arc consistency on the original problem. They can also be used to establish (i,j)-consistency on binary constraints. Experiments show that these encodings are an effective method for enforcing such consistencies, that can lead to a reduction in runtimes at the phase transition in most cases. Compared to the more traditional (direct) encoding, the search tree can be greatly pruned.