Certified SAT solving with GPU accelerated inprocessing

Abstract

Since 2013, the leading SAT solvers in SAT competitions all use inprocessing, which, unlike preprocessing, interleaves search with simplifications. However, inprocessing is typically a performance bottleneck, in particular for hard or large formulas. In this work, we introduce the first attempt to parallelize inprocessing on GPU architectures. As one of the main challenges in GPU programming is memory locality, we present new compact data structures and devise a data-parallel garbage collector. It runs in parallel on the GPU to reduce memory consumption and improve memory locality. Our new parallel variable elimination algorithm is roughly twice as fast as previous work. Moreover, we augment the variable elimination with the first parallel algorithm for functional dependency extraction in an attempt to find more logical gates to eliminate that cannot be found with syntactic approaches. We present a novel algorithm to generate clausal proofs in parallel to validate all simplifications running on the GPU besides the CDCL search, giving high credibility to our solver and its use in critical applications such as model checkers. In experiments, our new solver ParaFROST solves numerous benchmarks faster on the GPU than its sequential counterparts. With functional dependency extraction, inprocessing in ParaFROST was more effective in reducing the solving time. Last but not least, all proofs generated by ParaFROST were successfully verified.

The fast and the capacious: memory-efficient multi-GPU accelerated explicit state space exploration with GPUexplore 3.0

“…Major advances in computation increasingly need to be obtained via parallel software as Moore's Law comes to an end (Leiserson et al, 2020). In the last decade, GPUs have been successfully applied to accelerate various computations relevant for model checking, such as probability computations for probabilistic model checking (Bošnački et al, 2011;Wijs and Bošnački, 2012;Khan et al, 2021), counter-example construction (Wu et al, 2014), state space decomposition (Wijs et al, 2016a), parameter synthesis for stochastic systems ( Češka et al, 2016), and SAT solving (Youness et al, 2015(Youness et al, , 2020Osama et al, 2018Osama et al, , 2023Osama andWijs, 2019a,b, 2021;Prevot et al, 2021;Osama, 2022). VOXLOGICA-GPU applies model checking to analyse (medical) images (Bussi et al, 2021).…”