TurboSAT: Gradient-Guided Boolean Satisfiability Accelerated on GPU-CPU Hybrid System

TL;DR

TurboSAT introduces a hybrid GPU-CPU approach that combines differentiable optimization and traditional search to significantly accelerate Boolean SAT solving, achieving over 200x speedups on benchmark problems.

Contribution

This work presents a novel formulation of SAT as a differentiable matrix multiplication, enabling GPU acceleration and hybrid optimization-sequential search for faster SAT solving.

Findings

Achieves up to 200x speedup over CPU-based solvers.

Effectively combines differentiable optimization with conflict-driven search.

Demonstrates scalability on benchmark SAT problems.

Abstract

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.