We solve constraint satisfaction problems through translation to answer set programming (ASP). Our reformulations have the property that unit-propagation in the ASP solver achieves well defined local consistency properties like arc, bound and range consistency. Experiments demonstrate the computational value of this approach.
@cite_24: We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudo-Boolean solver.
@cite_22: We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the ALLDIFFERENT constraint.
Decompositions of all-different into simple arithmetic constraints such that bound and range consistency can be achieved were proposed in @cite_24 . There is no polynomial-sized decomposition that achieves domain consistency @cite_22 .