Abstract Recently, a continuous-time, deterministic analog solver based on ordinary differential equations (CTDS) was introduced, to solve Boolean satisfiability (SAT), a family of discrete constraint satisfaction problems. Since SAT is NP-complete, efficient algorithms would benefit solving a large number of decision type problems, both within industry and the sciences. Here we present a graphics processing units (GPU) based implementation of the CTDS and its variants and show that one can achieve significantly improved performance within a wide range of SAT problems. We present and discuss three versions of our GPU implementation and compare their performance to CPU implementations, showing an improvement factor of up to two orders of magnitude. We illustrate the performance of our GPU-based solver on random SAT problems and a notoriously difficult graph coloring problem, the Ramsey number problem R ( 3 , 3 , 3 , 3 ) , and compare it with the state-of-the-art SAT solver MiniSAT’s performances on CPUs.

中文翻译：

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使用 GPU 加速连续时间模拟 SAT 求解器

摘要 最近，引入了一种基于常微分方程（CTDS）的连续时间确定性模拟求解器，用于求解布尔可满足性（SAT），这是一个离散约束满足问题族。由于 SAT 是 NP 完全的，高效的算法将有利于解决工业和科学领域的大量决策类型问题。在这里，我们展示了基于图形处理单元 (GPU) 的 CTDS 及其变体的实现，并表明可以在广泛的 SAT 问题中显着提高性能。我们展示并讨论了我们 GPU 实现的三个版本，并将它们的性能与 CPU 实现进行了比较，显示了高达两个数量级的改进因子。