An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams

We prove an exponential lower bound on the size of proofs in the proof system operating with ordered binary decision diagrams introduced by Atserias, Kolaitis and Vardi [2]. In fact, the lower bound applies to semantic derivations operating with sets defined by OBDDs. We do not assume any particular format of proofs or ordering of variables, the hard formulas are in CNF. We utilize (somewhat indirectly) feasible interpolation. Atserias, Kolaitis and Vardi [2] generalized refutation proof systems from Boolean logic to the realm of Constraint Satisfaction Problems (CSP), viewing it as a special case of constraint propagation. This brings constraint propagation within the reach of proof complexity methods and, on the other hand, introduces a new class of propositional proof systems (pps) in the sense of Cook and Reckhow [6]. In the Boolean case Atserias et.al. [2] introduced and studied a particular pps operating with ordered binary decision diagrams (OBDD), and they obtained a number of proof complexity results about it. In particular, they compared the pps with several well-known pps’, including resolution, constant-depth Frege systems and small-coefficients cutting planes. A problem left open in Atserias et.al.[2] is to prove a lower bound for this new pps, although they have obtained an interesting partial result: a feasible interpolation theorem (also monotone, and hence a lower bound