Monotone Literals and Learning in QBF Reasoning

Monotone literal fixing (MLF) and learning are well-known lookahead and lookback mechanisms in propositional satisfiability (SAT) . When considering Quantified Boolean Formulas (QBFs), their separate implementation leads to significant speed-ups in state-of-the-art DPLL-based solvers. This paper is dedicated to the efficient implementation of MLF in a QBF solver with learning. The interaction between MLF and learning is far from being obvious, and it poses some nontrivial questions about both the detection and the propagation of monotone literals. Complications arise from the presence of learned constraints, and are related to the question about whether learned constraints have to be considered or not during the detection and/or propagation of monotone literals. In the paper we answer to this question both from a theoretical and from a practical point of view. We discuss the advantages and the disadvantages of various solutions, and show that our solution of choice, implemented in our solver QUBE, produces significant speed-ups in most cases. Finally, we show that MLF can be fundamental also for solving some SAT instances, taken from the 2002 SAT solvers competition.