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In 2006, Biere, Jussila, and Sinz made the key observation that theunderlying logic behind algorithms for constructing Reduced, Ordered BinaryDecision Diagrams (BDDs) can be encoded as steps in a proof in the extendedresolution logical framework. Through this, a BDD-based Boolean satisfiability(SAT) solver can generate a checkable proof of unsatisfiability for a set ofclauses. Such a proof indicates that the formula is truly unsatisfiable withoutrequiring the user to trust the BDD package or the SAT solver built on top ofit.  We extend their work to enable arbitrary existential quantification of theformula variables, a critical capability for BDD-based SAT solvers. Wedemonstrate the utility of this approach by applying a BDD-based solver,implemented by modifying an existing BDD package, to several challengingBoolean satisfiability problems. Our resultsdemonstrate scaling for parityformulas, as well as the Urquhart, mutilated chessboard, and pigeonholeproblems far beyond that of other proof-generating SAT solvers.

Generating Extended Resolution Proofs with a BDD-Based SAT Solver