We study parallel algorithms for the minimization of Deterministic Finite Automata (DFAs). In particular, we implement four different massively parallel algorithms on Graphics Processing Units (GPUs). Our results confirm the expectations that the algorithm with the theoretically best time complexity is not practically suitable to run on GPUs due to the large amount of resources needed. We empirically verify that parallel partition refinement algorithms from the literature perform better in practice, even though their time complexity is worse. Lastly, we introduce a novel algorithm based on partition refinement with an extra parallel partial transitive closure step and show that on specific benchmarks it has better run-time complexity and performs better in practice.

翻译：本研究探讨确定性有限自动机最小化的并行算法。具体而言，我们在图形处理器上实现了四种不同的大规模并行算法。实验结果表明，理论时间复杂度最优的算法因所需资源量过大而不适合在GPU上实际运行。我们通过实证验证，文献中基于并行分区细化的算法在实践中表现更优，尽管其时间复杂度较差。最后，我们提出一种基于分区细化的新型算法，该算法引入额外的并行偏传递闭包步骤，并在特定基准测试中展现出更优的时间复杂度与实践性能。