An elegant strategy for proving impossibility results in distributed computing was introduced in the celebrated FLP consensus impossibility proof. This strategy is local in nature as at each stage, one configuration of a hypothetical protocol for consensus is considered, together with future valencies of possible extensions. This proof strategy has been used in numerous situations related to consensus, leading one to wonder why it has not been used in impossibility results of two other well-known tasks: set agreement and renaming. This paper provides an explanation of why impossibility proofs of these tasks have been of a global nature. It shows that a protocol can always solve such tasks locally, in the following sense. Given a configuration and all its future valencies, if a single successor configuration is selected, then the protocol can reveal all decisions in this branch of executions, satisfying the task specification. This result is shown for both set agreement and renaming, implying that there are no local impossibility proofs for these tasks.

中文翻译：

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局部可解决的任务和价位参数的局限性

在著名的FLP共识不可能证明中引入了一种证明分布式计算不可能结果的优雅策略。这种策略本质上是局部的，因为在每个阶段，都考虑了一种用于达成共识的假设协议的配置，以及未来可能的扩展价。这种证明策略已在与共识相关的许多情况下使用，这使人们想知道为什么未在另外两项众所周知的任务的可能性结果中使用它：设置协议和重命名。本文解释了为什么这些任务的不可能证明具有全球性。它表明，从以下意义上讲，协议可以始终在本地解决此类任务。给定配置及其所有未来效价，如果选择单个后继配置，然后协议可以揭示执行分支中的所有决策，从而满足任务规范。既定约定和重命名都显示了此结果，这意味着这些任务没有本地不可能的证明。