TurboSAT: Gradient-Guided Boolean Satisfiability Accelerated on GPU-CPU Hybrid System
This addresses scalability issues in logical reasoning for applications like verification and AI, though it is incremental as it builds on existing SAT solving methods.
The paper tackled the limited parallelism in Boolean satisfiability (SAT) solving by formulating it as a differentiable optimization problem, enabling a hybrid GPU-CPU system that achieved runtime speedups of over 200x compared to a state-of-the-art CPU solver on public benchmarks.
While accelerated computing has transformed many domains of computing, its impact on logical reasoning, specifically Boolean satisfiability (SAT), remains limited. State-of-the-art SAT solvers rely heavily on inherently sequential conflict-driven search algorithms that offer powerful heuristics but limit the amount of parallelism that could otherwise enable significantly more scalable SAT solving. Inspired by neural network training, we formulate the SAT problem as a binarized matrix-matrix multiplication layer that could be optimized using a differentiable objective function. Enabled by this encoding, we combine the strengths of parallel differentiable optimization and sequential search to accelerate SAT on a hybrid GPU-CPU system. In this system, the GPUs leverage parallel differentiable solving to rapidly evaluate SAT clauses and use gradients to stochastically explore the solution space and optimize variable assignments. Promising partial assignments generated by the GPUs are post-processed on many CPU threads which exploit conflict-driven sequential search to further traverse the solution subspaces and identify complete assignments. Prototyping the hybrid solver on an NVIDIA DGX GB200 node, our solver achieves runtime speedups up to over 200x when compared to a state-of-the-art CPU-based solver on public satisfiable benchmark problems from the SAT Competition.