Synchronizing sequences for large-scale automata have gained popularity recently due to their practical use cases especially to have a faster and better testing process. In many applications, shorter sequences imply less overhead and faster processing time but the problem of finding the shortest synchronizing sequence is NP-hard and requires heuristic approaches to be solved. State-of-the-art heuristics manage to obtain desirable, short sequences with relatively small execution times. However, all these heuristics suffer their quadratic memory complexity and fail to scale when the input automaton gets larger. In this paper, we propose an approach exploiting GPUs and hybrid parallelism which can generate synchronizing sequences even for billion-scale automata, in a short amount of time. Overall, the algorithm can generate a synchronizing sequence for a random automaton with $n={10}^8$ states in 12.1 s, $n=5\times {10}^8$ states in 69.1 s, and billion states in 148.2 s.

大规模自动机的同步序列最近因其实际用例而广受欢迎，尤其是具有更快更好的测试过程。在许多应用中，较短的序列意味着更少的开销和更快的处理时间，但找到最短同步序列的问题是 NP-hard 问题，需要启发式方法来解决。最先进的启发式方法设法以相对较短的执行时间获得所需的短序列。然而，当输入自动机变大时，所有这些启发式算法都会受到二次内存复杂性的影响，并且无法扩展。在本文中，我们提出了一种利用 GPU 和混合并行性的方法，即使对于十亿级自动机，它也可以在短时间内生成同步序列。全面的，$n={10}^8$ 状态在 12.1 秒， $n=5\times {10}^8$ 状态在 69.1 秒，十亿个状态在 148.2 秒。