Massively Parallel Continuous Local Search for Hybrid SAT Solving on GPUs

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 achieved by a 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. FastFourierSAT is compared with a wide set of SOTA parallel SAT solvers on extensive benchmarks including combinatorial and industrial problems. Results show that FastFourierSAT computes the gradient 100+ times faster than previous prototypes on CPU. Moreover, FastFourierSAT solves most instances and demonstrates promising performance on larger-size instances.