Unified QBF Certification and its Applications
Journal
Formal Methods in System Design (FMSD)
Journal Volume
41
Journal Issue
1
Pages
45-65
Date Issued
2012-08
Author(s)
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. To date the certificate of a true formula can be in the form of either a syntactic cube-resolution proof or a semantic Skolem-function model whereas that of a false formula is only in the form of a syntactic clause-resolution proof. The semantic certificate for a false QBF is missing, and the syntactic and semantic certificates are somewhat unrelated. This paper identifies the missing Herbrand-function countermodel for false QBF, and strengthens the connection between syntactic and semantic certificates 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 special Skolemization-based solvers and computed from standard search-based ones. Experimental results show strong benefits of the new method. © 2012 Springer Science+Business Media, LLC.
Type
journal article