The Oracular Constraints Method

Constraint satisfaction and combinatorial optimization form the crux of many AI problems. In constraint satisfaction, feasibility-reasoning mechanisms are used to prune the search space, while optimality-reasoning is used for combinatorial optimization. Many AI tasks related to diagnosis, trajectory tracking and planning can be formulated as hybrid problems containing both satisfaction and optimization components, and can greatly benefit from a proper blend of these independently powerful techniques. We introduce the notion of model counting to bridge the gap between feasibilityand optimality-reasoning. The optimization part of a problem then becomes a search for the right set of constraints that must be satisfied in any good solution. These constraints, which we call the oracular constraints, replace the optimization component of a problem to revive the power of constraint reasoning systems.