SAT Solving with GPU Accelerated Inprocessing

Abstract

Since 2013, the leading SAT solvers in the SAT competition all use inprocessing, which unlike preprocessing, interleaves search with simplifications. However, applying inprocessing frequently can still be a bottle neck, i.e., for hard or large formulas. In this work, we introduce the first attempt to parallelize inprocessing on GPU architectures. As memory is a scarce resource in GPUs, we present new space-efficient data structures and devise a data-parallel garbage collector. It runs in parallel on the GPU to reduce memory consumption and improves memory access locality. Our new parallel variable elimination algorithm is twice as fast as previous work. In experiments our new solver ParaFROST solves many benchmarks faster on the GPU than its sequential counterparts.

GPU Acceleration of Bounded Model Checking with ParaFROST

“…We present the SAT solver ParaFROST that applies Conflict Driven Clause Learning (CDCL) [26] with GPU acceleration of pre-and inprocessing [32][33][34], tuned for BMC. It has been implemented in CUDA C++ v11 [28], is based on CaDiCaL [6], and interfaces with CBMC.…”

“…Second of all, we introduce memory-aware variable elimination, to avoid running out of memory due to adding too many new clauses. In practice, we experienced this problem when applying the original procedure of [34] for BMC.…”

“…Additionally, to support BMC, ParaFROST must be an incremental solver, i.e., it must exploit that a number of very similar SAT problems are solved in sequence [16]. The procedure in [34] does not support this, so we extended it.…”

“…Recently, GPUs have been applied for explicit-state model checking and graph analysis [8,9,40,41]. In SAT solving, we used GPUs to accelerate test pattern generation [31], metaheuristic search [42], preprocessing [32,33] and inprocessing [34]. In these operations, a given SAT formula is simplified, i.e., it is rewritten to a formula with fewer variables and/or clauses, while preserving satisfiability, using various simplification rules.…”

“…In preprocessing, this is only done once before the solving starts, while in inprocessing, this is done periodically during the solving. While the impact of accelerating these procedures has been demonstrated [34], its impact on BMC has not yet been addressed.…”