The wakeup problem in distributed computing asks for a symmetric protocol that enables one of several processors to eventually guarantee that all (or, in a more general setting, enough) other processors have acted, using a shared register but no global clock. Dropping the symmetry requirement gives a well-known exercise often phrased in terms of prisoners entering, in an unknown sequence, a room equipped with a single binary switch, and using it to communicate. Kane and Kominers recently analysed a more general version of the latter with multiple parallel and indistinguishable rooms. We answer some open questions of Kane and Kominers regarding the minimum number of switch states needed for the prisoners to solve the problem. We also consider the symmetric ``wakeup'' version of this scenario, and establish exactly for which numbers of processors and registers a solution is possible.

翻译：分布式计算中的唤醒问题要求设计一种对称协议，使得多个处理器之一能够通过共享寄存器（无全局时钟）最终确保所有（或更一般情形下，足够数量的）其他处理器均已执行操作。若不要求对称性，该问题可简化为一个经典习题：囚犯以未知顺序依次进入一个配备单个二进制开关的房间，并利用该开关进行通信。Kane与Kominers最近分析了后者在多个平行且不可区分房间场景下的广义版本。我们解答了Kane与Kominers提出的若干开放问题，涉及囚犯解决该问题所需的最小开关状态数。此外，我们探讨了该场景的对称“唤醒”版本，并精确确定了在哪些处理器与寄存器的数量组合下可存在解决方案。