Leveraging GPUs for Effective Clause Sharing in Parallel SAT Solving

Abstract

The past two decades have witnessed an unprecedented improvement in runtime performance of SAT solvers owing to clever software engineering and creative design of data structures. Yet, most entries in the annual SAT competition retain the core architecture of MiniSat, which was designed from the perspective of single core CPU architectures. Since 2005, however, there has been a significant shift to heterogeneous architectures owing to the impending end of Dennard scaling.

The primary contribution of this work is a novel multi-threaded CDCL-based framework, called $\mathsf {GPUShareSat}$, designed to take advantage of CPU+GPU architectures. The core underlying principle of our approach is to divide the tasks among the CPU and the GPU so as to attempt to achieve the best of both worlds. We observe that bit-vector based operations can allow a GPU to efficiently determine the usefulness of a learnt clause to different threads and accordingly notify the thread of the presence of relevant clauses. This approach of checking all clauses against all assignments from different threads allows the GPU to exploit its potential for massive parallelism through clever group-testing strategy and bitwise operations.

Our detailed empirical analysis shows practical efficiency of our approach: in particular, $\mathsf {GPUShareSat}$ augmented with the state-of-the-art single-threaded solver Relaxed_LCMDCBDL_newTech solved 19 more instances than the winner of the 2020 SAT competition’s parallel track, P-MCOMSPS-STR.

The accompany open source library is available at https://github.com/nicolasprevot/GpuShareSat.

N. Prevot—Independent Researcher.