Massively Parallel Continuous Local Search for Hybrid SAT Solving on GPUs

TL;DR

FastFourierSAT introduces a GPU-accelerated hybrid SAT solver using gradient-driven local search with a novel parallel algorithm inspired by FFT, significantly improving speed and scalability over previous methods.

Contribution

The paper presents a new parallel algorithm for continuous local search in SAT solving, enabling efficient GPU acceleration and improved performance over existing CLS approaches.

Findings

FastFourierSAT computes gradients 100+ times faster than CPU-based prototypes.

It solves most benchmark instances and scales well to larger problems.

The approach outperforms state-of-the-art parallel SAT solvers on several benchmarks.

Abstract

Although state-of-the-art (SOTA) SAT solvers based on conflict-driven clause learning (CDCL) have achieved remarkable engineering success, their sequential nature limits the parallelism that may be extracted for acceleration on platforms such as the graphics processing unit (GPU). In this work, we propose FastFourierSAT, a highly parallel hybrid SAT solver based on gradient-driven continuous local search (CLS). This is realized by a novel parallel algorithm inspired by the Fast Fourier Transform (FFT)-based convolution for computing the elementary symmetric polynomials (ESPs), which is the major computational task in previous CLS methods. The complexity of our algorithm matches the best previous result. Furthermore, the substantial parallelism inherent in our algorithm can leverage the GPU for acceleration, demonstrating significant improvement over the previous CLS approaches. We also propose to incorporate the restart heuristics in CLS to improve search efficiency. We compare our approach with the SOTA parallel SAT solvers on several benchmarks. Our results show that FastFourierSAT computes the gradient 100+ times faster than previous prototypes implemented on CPU. Moreover, FastFourierSAT solves most instances and demonstrates promising performance on larger-size instances.