Partial witnesses from preprocessed quantified Boolean formulas

For effectively solving quantified Boolean formulas (QBFs), preprocessors have shown to be of great value. A preprocessor rewrites a formula such that helpful information is made explicit and irrelevant information is removed. For this purpose, techniques, which would be too costly when repeatedly applied during the solving process, are used. Unfortunately, most preprocessing techniques are not model preserving and therefore incompatible with certification frameworks. In consequence, the application of a preprocessor prohibits the extraction of witnesses encoding a solution or a counterexample of a formula. In this paper, we show how to obtain partial witnesses from preprocessed QBFs. Partial witnesses are assignments for the variables of the outermost quantifier block and are extensible to full witnesses, which are usually represented as functions reflecting the dependencies between variables. For many applications, however, partial witnesses are sufficient. We modified the publicly available preprocessor bloqqer for extracting partial witnesses. We empirically compare the effectiveness of the modified and the original version of bloqqer. Further, we apply the new version of bloqqer for solving hardware synthesis problems for which it turns out to be extremely beneficial.