Conformant planning as a case study of incremental QBF solving

We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of successively constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase as well as in the solving phase. We also present experiments with incremental preprocessing techniques that are based on blocked clause elimination (QBCE). QBCE allows to eliminate certain clauses from a QBF in a satisfiability preserving way. We implemented the QBCE-based techniques in DepQBF in three variants: as preprocessing, as inprocessing (which extends preprocessing by taking into account variable assignments that were fixed by the QBF solver), and as a novel dynamic approach where QBCE is tightly integrated in the solving process. For DepQBF, experimental results show that incremental QBF solving with incremental QBCE outperforms incremental QBF solving without QBCE, which in turn outperforms nonincremental QBF solving. For the first time we report on incremental QBF solving with incremental QBCE as inprocessing. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.