In 2006, Biere, Jussila, and Sinz made the key observation that the
underlying logic behind algorithms for constructing Reduced, Ordered Binary
Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended
resolution logical framework. Through this, a BDD-based Boolean satisfiability
(SAT) solver can generate a checkable proof of unsatisfiability for a set of
clauses. Such a proof indicates that the formula is truly unsatisfiable without
requiring the user to trust the BDD package or the SAT solver built on top of
it.
We extend their work to enable arbitrary existential quantification of the
formula variables, a critical capability for BDD-based SAT solvers. We
demonstrate the utility of this approach by applying a prototype solver to
several problems that are very challenging for search-based SAT solvers,
obtaining polynomially sized proofs on benchmarks for parity formulas, as well
as the Urquhart, mutilated chessboard, and pigeonhole problems.Comment: Extended version of paper published at TACAS 202