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.

中文翻译：

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使用基于BDD的SAT解算器生成扩展分辨率证明

在2006年，Biere，Jussila和Sinz做出了关键观察，即在扩展分辨率逻辑框架中，用于构造精简有序二元决策图（BDD）的算法背后的基本逻辑可以作为证明中的步骤进行编码。通过这种方式，基于BDD的布尔可满足性（SAT）求解器可以生成一组子句的不可满足性的可检查证明。这样的证明表明，在不要求用户信任BDD包或基于BDD包的SAT求解器的情况下，该公式确实是无法满足的。我们扩展了他们的工作，以实现公式变量的任意存在量化，这是基于BDD的SAT求解器的一项关键功能。我们通过将原型求解器应用于一些对于基于搜索的SAT求解器非常具有挑战性的问题，证明了这种方法的实用性，