Accelerated Fourier SAT (AFSAT): Fully Realising a GPU-based Symmetric Pseudo-Boolean SAT Solver
Quick Answer
This paper shows that Accelerated Fourier SAT (AFSAT) is a GPU-accelerated pseudo-Boolean SAT solver that enhances runtime performance and memory efficiency through continuous local search and JAX's capabilities.
Quick Take
Accelerated Fourier SAT (AFSAT) is a GPU-accelerated pseudo-Boolean SAT solver that enhances runtime performance and memory efficiency through continuous local search and JAX's capabilities. It addresses floating-point limitations with a discrete Fourier transform implementation, achieving near-linear throughput across multiple accelerators.
Key Points
- AFSAT is built on the FastFourierSAT proof-of-concept.
- Utilizes JAX for automatic vectorization and just-in-time compilation.
- Improves numerical stability and runtime performance significantly.
- Addresses memory latency and floating-point representation issues.
- Achieves near-linear throughput with JAX array sharding.
Article Content
From source RSS / original summaryarXiv:2606. 06641v1 Announce Type: new Abstract: We present Accelerated Fourier SAT (AFSAT), a GPU-accelerated solver for pseudo-Boolean satisfiability based on continuous local search (CLS). AFSAT realises the proof-of-concept approach, FastFourierSAT, into a fully-engineered solver supporting any heterogeneous mixture of symmetric constraint types and lengths within a single problem instance.
Using the JAX compiler, AFSAT leverages pure function composition, automatic vectorisation, automatic differentiation, and just-in-time (JIT) compilation to perform massively parallel CLS across batches of candidate assignments. We demonstrate substantially improved numerical stability, runtime performance, and memory efficiency over the proof-of-concept.
We achieve this by way of identifying and addressing various limitations that arise from memory latency and floating-point representation, as well as leveraging automatic parallelisation and compact representations. The inherent representational and stability limitations of floating point are partially addressed by a tailored discrete Fourier transform implementation. We achieve near-linear throughput when scaling to multiple accelerators via JAX array sharding.
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