The cost of communication is a substantial factor affecting the scalability of many distributed applications. Every message sent can incur a cost in storage, computation, energy, and bandwidth. Consequently, reducing the communication costs of distributed applications is highly desirable. The best way to reduce message costs is by communicating without sending any messages whatsoever. This article initiates a rigorous investigation into the use of silence in synchronous settings, in which processes can fail. We formalize sufficient conditions for information transfer using silence, as well as necessary conditions for particular cases of interest. This allows us to identify message patterns that enable communication through silence. In particular, a pattern called a silent choir is identified, and shown to be central to information transfer via silence in failure-prone systems. The power of the new framework is demonstrated on the atomic commitment problem (AC). A complete characterization of the tradeoff between message complexity and round complexity in the synchronous model with crash failures is provided, in terms of lower bounds and matching protocols. In particular, a new message-optimal AC protocol is designed using silence, in which processes decide in three rounds in the common case. This significantly improves on the best previously known message-optimal AC protocol, in which decisions were performed in Θ( n ) rounds. And in the naked light I saw Ten thousand people, maybe more People talking without speaking … People writing songs that voices never share And no one dared Disturb the sound of silence Paul Simon, 1964

中文翻译：

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安静

通信成本是影响许多分布式应用程序可扩展性的重要因素。发送的每条消息都会产生存储、计算、能源和带宽方面的成本。因此，非常希望降低分布式应用程序的通信成本。降低消息成本的最佳方法是在不发送任何消息的情况下进行通信。本文对在同步设置中使用静默进行严格调查，其中进程可能会失败。我们使用沉默形式化了信息传递的充分条件，以及特定感兴趣案例的必要条件。这使我们能够识别能够通过沉默进行通信的消息模式。特别是，一种称为无声合唱团被识别出来，并被证明是在容易发生故障的系统中通过静默进行信息传输的核心。新框架的力量体现在原子承诺问题（AC）。在下限和匹配协议方面，提供了具有崩溃失败的同步模型中消息复杂度和轮复杂度之间折衷的完整表征。特别是，使用静默设计了一种新的消息最优 AC 协议，其中进程在常见情况下分三轮决定。这显着改进了先前已知的最佳消息最优 AC 协议，其中决策在 Θ(n) 回合。在我看到的赤裸的光中 一万人，也许更多 人们说话不说话…写歌的人永远不会分享声音 而且没人敢 打扰寂静的声音保罗·西蒙，1964