AI 中文总结
本文将随机广播模型下二进制共识的研究从2个进程扩展至n>2的场景，旨在设计r轮内终止、最小化错误分歧概率的共识算法。
AI 中文摘要
我们研究随机广播模型下的二进制共识问题，该模型假设存在n≥2个进程通过消息广播进行同步通信，每一轮中每个进程向其他所有进程广播一条消息，每次广播以概率p∈[0,1]独立成功：若成功，所有进程均接收该消息；若失败，无进程接收该消息，且发送方无法知晓广播是否成功。在该模型中，共识问题不可解，目标是针对给定的轮数r，设计在r轮内终止的共识算法，以最小化错误分歧的概率。此前已有研究针对2个进程的情况（发表于DISC 2025），本文将该研究扩展至n>2的场景。
英文摘要
We study binary consensus in the \emph{stochastic broadcast model}, which assumes $n\geq 2$ processes communicating synchronously by message broadcasts. At each round, every process broadcasts a message to all the other processes. Each broadcast succeeds independently with some probability $p\in[0,1]$. If a broadcast succeeds, all processes receive the message, and if it fails, no process receives the message. The sender does not know whether its broadcast was successful or not. In this model, consensus is not solvable; the objective is to design, for a given number of rounds $r$, consensus algorithms that terminate in $r$ rounds, minimizing the probability of error disagreement. This problem has been studied in depth for 2 processes [DISC 2025]. We extend the study to $n> 2$.
