We demonstrate possibility for vector consensus under the model used by Fischer, Lynch, and Patterson (FLP) to prove impossibility of binary consensus - in full asynchrony and up to one unannounced faulty process. We also show that: i) figuring out a vector dataset is an inevitable phase of binary agreement; and ii) agreeing on a vector dataset is sufficient for binary agreement. Key finding: the FLP result proves impossibility the processes to always produce binary value from a figured-out dataset that contains less than the entire initial state, which causes the impossibility to terminate.
翻译:我们证明,在Fischer、Lynch和Patson(FLP)所使用的模式下,病媒共识有可能证明不可能达成二进制共识 -- -- 完全的无节奏和直至一个未宣布的错误过程。我们还表明:一)确定一个矢量数据集是二进制协议的一个不可避免的阶段;二)商定一个矢量数据集就足以达成二进制协议。关键发现:FLP结果证明,程序不可能总是从包含低于整个初始状态的集出数据集中产生二进制值,而最初状态又导致无法终止。