Near-optimal self-stabilising counting and firing squads,Distributed Computing

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Near-optimal self-stabilising counting and firing squads
Distributed Computing ( IF 1.3 ) Pub Date : 2018-09-12 , DOI: 10.1007/s00446-018-0342-6
Christoph Lenzen , Joel Rybicki

Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given $$C>1$$C>1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input. We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience $$f

中文翻译：

近乎最优的自稳定计数和行刑队

考虑一个由 n 个节点组成的全连接同步分布式系统，其中多达 f 个节点可能出现故障，并且每个节点都以任意初始状态开始。在同步 C 计数问题中，所有节点最终需要就一个计数器达成一致，该计数器在给定 $$C>1$$C>1 的每一轮中增加一个模 C。在自稳定行刑队问题中，任务是最终保证所有非故障节点对外部输入同时响应：如果正确节点的子集接收到外部“go”信号作为输入，那么所有正确节点都应该就一轮（在不久的将来）共同输出“开火”信号达成一致。此外，如果某个正确的节点之前接收到“go”信号作为输入，则任何节点都不应该生成“fire”信号。我们提出了一个框架，以非常小的成本将这两个任务简化为二元共识。例如，我们获得了具有最佳弹性 $$f 的自稳定拜占庭行刑队的确定性算法

更新日期：2018-09-12

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