Solution Learning and Solution Directed Backjumping, Revisited

We make two significant contributions. First, we introduce a new technique for solution based learning in Quantified Boolean Formulae (QBF’s.) This takes advantage of the structure of QBF’s to improve on previous methods. More information is extracted from each solution learnt, so fewer states need to be visited later in search. Unfortunately, our empirical results suggest that our learning technique does not do well on non-random benchmarks. Our second contribution is an important negative result which helps to explain this poor performance. We show empirically that solutiondirected backjumping (SBJ) provides little or no reduction in search on non-random instances from QBFLib, while it does cause an overhead. All solution learning methods exploit the power of SBJ, so neither our new method nor existing ones can be effective unless SBJ is. As well as explaining the lack of success of learning methods, this suggests that even SBJ may cause unnecessary overheads unless the existing set of benchmarks is inadequate. Finally, for random instances for which SBJ is effective, we show that our new learning technique can improve median universal backtracks by an order of magnitude and improve runtime by a factor of eight.