Abstract
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. Such proofs indicate 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 obtain polynomially sized proofs on benchmarks for the mutilated chessboard and pigeonhole problems—ones that are very challenging for search-based SAT solvers.
Keywords
- extended resolution
- binary decision diagrams
- mutilated chessboard
- pigeonhole problem
M. J. H. Heule—Supported by the National Science Foundation under grant CCF-2010951
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Bryant, R.E., Heule, M.J.H. (2021). Generating Extended Resolution Proofs with a BDD-Based SAT Solver. In: Groote, J.F., Larsen, K.G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2021. Lecture Notes in Computer Science(), vol 12651. Springer, Cham. https://doi.org/10.1007/978-3-030-72016-2_5
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