Resolution Proofs and Skolem Functions in QBF Evaluation and Applications

Abstract. Quantified Boolean formulae (QBF) allow compact encoding of many decision problems. Their importance motivated the development of fast QBF solvers. Certifying the results of a QBF solver not only ensures correctness, but also enables certain synthesis and verification tasks particularly when the certificate is given as a set of Skolem functions. To date the certificate of a true formula can be in the form of either a (cube) resolution proof or a Skolem-function model whereas that of a false formula is in the form of a (clause) resolution proof. The resolution proof and Skolem-function model are somewhat unrelated. This paper strengthens their connection by showing that, given a true QBF, its Skolem-function model is derivable from its cube-resolution proof of satisfiability as well as from its clause-resolution proof of unsatisfiability under formula negation. Consequently Skolem-function derivation can be decoupled from Skolemization-based solvers and computed from sta...

• Type: Journal
• Year: 2011
• Where: CAV
• Authors: Valeriy Balabanov, Jie-Hong R. Jiang
• Keywords: Boolean Formulae, CAV 2011, Clause Resolution, Hardware, Skolem Functions