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

2025-11-11

AI Summary

Traditional SAT solvers rely on sequential conflict-driven clause learning (CDCL), inherently limiting parallelization and hindering scalability on large-scale instances. This paper introduces the first differentiable SAT solving framework, reformulating Boolean satisfiability as a continuous optimization problem. We propose a differentiable encoding based on binarized matrix multiplication, construct a smooth objective function, and perform gradient-guided parallel search on GPUs. Crucially, we co-design a CPU-based conflict-driven learning mechanism to enable heterogeneous协同 optimization between GPU-accelerated continuous search and CPU-based discrete reasoning. Our approach breaks the fundamental sequentiality bottleneck of classical SAT solving. Evaluated on SAT Competition benchmarks, it achieves up to 200× speedup over state-of-the-art CPU-based solvers, significantly improving both scalability and hardware utilization.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Hardware-aware ML

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Accelerating Boolean satisfiability solving using hybrid GPU-CPU systems
• Combining parallel differentiable optimization with sequential conflict-driven search
• Overcoming parallelism limitations in traditional SAT solvers through gradient guidance

Innovation

• GPU-CPU hybrid system for parallel SAT solving
• Differentiable optimization using gradient-guided clause evaluation
• Binarized matrix encoding enabling stochastic solution exploration