# Accelerated Fourier SAT (AFSAT): Fully Realising a GPU-based Symmetric Pseudo-Boolean SAT Solver

arXiv: https://arxiv.org/abs/2606.06641 · HTML: https://mlsanity.com/paper/2606.06641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 10 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 2 of 2)

- [Optimistix: modular optimisation in JAX and Equinox](https://mlsanity.com/paper/2402.09983/) (2024)
- [Massively Parallel Continuous Local Search for Hybrid SAT Solving on GPUs](https://mlsanity.com/paper/2308.15020/) (2023)

## Abstract (arXiv)

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.