无色任务与基于扩展的证明
Colorless Tasks and Extension-Based Proofs
AI总结：
本文为无色任务在NIIS模型中无扩展性证明的不可能性给出了充要条件，并提出一种与具体任务无关的通用对抗策略，证明了色剖分的相关性质。
摘要：
扩展性证明的概念为价性论证（valency argument）的思想建模，该思想在分布式计算中被广泛使用。扩展性证明的能力是有限的：已有研究表明，对于 $n > k \geq 2$ 个进程之间的 $(n,k)$-集合协商问题，不存在基于扩展的证明来证明无等待协议的不可能性。由于这些工作中的技术紧密依赖于具体任务，因此仅有少数任务已被证明其不可能性不存在基于扩展的证明。我们给出了在NIIS模型中，无色任务不存在无等待协议不可能性的基于扩展的证明的充分必要条件。我们引入了一种与任何具体任务规范解耦的通用对抗策略。在该策略中，我们证明了分布式计算中广泛使用的色剖分（chromatic subdivision）的若干性质。
英文摘要：
The concept of extension-based proofs models the idea of a valency argument, which is widely used in distributed computing. Extension-based proofs are limited in power: it has been shown that there is no extension-based proof of the impossibility of a wait-free protocol for $(n,k)$-set agreement among $n > k \geq 2$ processes. There are only a few tasks that have been proven to have no extension-based proof of the impossibility, since the techniques in these works are closely related to the specific task. We give a necessary and sufficient condition for colorless tasks to have no extension-based proofs of the impossibility of wait-free protocols in the NIIS model. We introduce a general adversarial strategy decoupled from any concrete task specification. In this strategy, some properties of the chromatic subdivision that is widely used in distributed computing are proved.
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