SIAM Journal on Computing, Ahead of Print.
In the consensus problem, there are $n$ processes that each has a private input value. Each nonfaulty process must output a single value such that no two processes output different values and the output is the input value of some process. There are many consensus protocols for systems where the processes may only communicate by reading and writing to shared registers. Of particular interest are protocols that have progress guarantees such as randomized wait-freedom or obstruction-freedom. In 1992, it was proved that such protocols must use $\Omega(\sqrt{n})$ registers. In 2015, this was improved to $\Omega(n)$ registers in the anonymous setting, where processes do not have identifiers. We prove that every randomized wait-free or obstruction-free protocol for solving consensus among $n$ processes must use at least $n-1$ registers.

中文翻译：

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达成共识的狭窄空间

《 SIAM计算杂志》，预印本。
在共识问题中，存在$ n $个过程，每个过程都有一个私有输入值。每个无故障的进程都必须输出一个值，这样就不会有两个进程输出不同的值，并且输出是某个进程的输入值。对于系统而言，有许多共识协议，其中进程只能通过读写共享寄存器进行通信。特别令人感兴趣的是具有进度保证的协议，例如随机的等待自由或阻塞自由。在1992年，事实证明，此类协议必须使用$ \ Omega（\ sqrt {n}）$寄存器。在2015年，它被改进为匿名设置中的$ \ Omega（n）$寄存器，其中进程没有标识符。我们证明，用于解决$ n $进程之间共识的每个随机无等待或无障碍协议都必须至少使用$ n-1 $寄存器。