  Recent achievements from AlphaZero using self-play has shown remarkable
performance on several board games. It is plausible to think that self-play,
starting from zero knowledge, can gradually approximate a winning strategy for
certain two-player games after an amount of training. In this paper, we try to
leverage the computational power of neural Monte Carlo Tree Search (neural
MCTS), the core algorithm from AlphaZero, to solve Quantified Boolean Formula
Satisfaction (QSAT) problems, which are PSPACE complete. Knowing that every
QSAT problem is equivalent to a QSAT game, the game outcome can be used to
derive the solutions of the original QSAT problems. We propose a way to encode
Quantified Boolean Formulas (QBFs) as graphs and apply a graph neural network
(GNN) to embed the QBFs into the neural MCTS. After training, an off-the-shelf
QSAT solver is used to evaluate the performance of the algorithm. Our result
shows that, for problems within a limited size, the algorithm learns to solve
the problem correctly merely from self-play.
