Solving QSAT problems with neural MCTS

TL;DR

This paper explores using neural Monte Carlo Tree Search, inspired by AlphaZero, to solve QSAT problems by encoding QBFs as graphs and applying GNNs, demonstrating successful self-play learning on small instances.

Contribution

It introduces a novel approach combining neural MCTS and GNNs to tackle QSAT problems, a significant step towards applying game-playing AI techniques to logic problems.

Findings

Algorithm learns to solve small QSAT problems from self-play

Neural MCTS with GNN encoding effectively models QBFs

Potential for scaling to larger problems with further development

Abstract

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.