Refutation proofs can be viewed as a special case of constraint propagation, which is a fundamental technique in solving constraint-satisfaction problems. The generalization lifts, in a uniform way, the concept of refutation from Boolean satisfiability problems to general constraint-satisfaction problems. On the one hand, this enables us to study and characterize basic concepts, such as refutation width, using tools from finite-model theory. On the other hand, this enables us to introduce new proof systems, based on representation classes, that have not been considered up to this point. We consider ordered binary decision diagrams (OBDDs) as a case study of a representation class for refutations, and compare their strength to well-known proof systems, such as resolution, the Gaussian calculus, cutting planes, and Frege systems of bounded alternation-depth. In particular, we show that refutations by ODBBs polynomially simulate resolution and can be exponentially stronger.
Joint work with Albert Atserias and Phokion Kolaitis.