An Effective QBF Solver for Planning Problems

A large number of applications can be represented by quantified Boolean formulas (QBF). Although evaluating QBF is NP-hard and thus very difficult, there has been significant progress in the development of QBF solvers. These solvers require the quantified Boolean formula to be in a standard format. We have encountered a large class of problems whose representation as QBF is not in that standard format. If we apply current state-of-the-art QBF solvers, the required transformation into standard format increases the size of the formula and tends to hide structural properties of the problem class. We suggest a direct attack of the problem. The solution algorithm is based on backtracking search and on a new form of learning clauses. We have tested a first implementation of the algorithm on a class of planning problems. The tests show that the approach is significantly faster than current state-of-the-art QBF solvers.