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Modern solvers for quantified Boolean formulas (QBF) not only decide the satisfiability of a formula, but also return a set of Skolem functions representing a model for a true QBF. Unfortunately, in combination with a preprocessor this ability is lost for many preprocessing techniques. A preprocessor rewrites the input formula to an equi-satisfiable formula which is often easier to solve than the original formula. Then the Skolem functions returned by the solver represent a solution for the preprocessed formula, but not necessarily for the original encoding. Our solution to this problem is to combine Skolem functions obtained from a QRAT trace as produced by the widely-used preprocessor Bloqqer with Skolem functions for the preprocessed formula. This approach is agnostic of the concrete rewritings performed by the preprocessor and allows the combination of Bloqqer with any Skolem function producing solver, hence realizing a smooth integration into the solving tool chain.

Learning and backjumping are essential features in search-based decision procedures for Quantified Boolean Formulas (QBF). To obtain a better understanding of such procedures, we present a formal framework, which allows to simultaneously reason on prenex conjunctive and disjunctive normal form. It captures both satisfying and falsifying search states in a symmetric way. This symmetry simplifies the framework and offers potential for further variants.

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