Failed literal detection for QBF

Abstract

Failed literal detection (FL) in SAT is a powerful approach for preprocessing. The basic idea is to assign a variable as assumption. If boolean constraint propagation (BCP) yields an empty clause then the negated assumption is necessary for satisfiability. Whereas FL is common in SAT, it cannot easily be applied to QBF due to universal quantification. We present two approaches for FL to preprocess prenex CNFs. The first one is based on abstraction where certain universal variables are treated as existentially quantified. Second we combine QBF-specific BCP (QBCP) in FL with Q-resolution to validate assignments learnt by FL. Finally we compare these two approaches to a third common approach based on SAT. It turns out that the three approaches are incomparable. Experimental evaluation demonstrates that FL for QBF can improve the performance of search- and elimination-based QBF solvers. © 2011 Springer-Verlag.