How to efficiently and reliably spread information in a system is one of the most fundamental problems in distributed computing. Recently, inspired by biological scenarios, several works focused on identifying the minimal communication resources necessary to spread information under faulty conditions. Here we study the self-stabilizing bit-dissemination problem, introduced by Boczkowski, Korman, and Natale in [SODA 2017]. The problem considers a fully-connected network of n agents, with a binary world of opinions, one of which is called correct. At any given time, each agent holds an opinion bit as its public output. The population contains a source agent which knows which opinion is correct. This agent adopts the correct opinion and remains with it throughout the execution. We consider the basic \(\mathcal {PULL}\) model of communication, in which each agent observes relatively few randomly chosen agents in each round. The goal of the non-source agents is to quickly converge on the correct opinion, despite having an arbitrary initial configuration, i.e., in a self-stabilizing manner. Once the population converges on the correct opinion, it should remain with it forever. Motivated by biological scenarios in which animals observe and react to the behavior of others, we focus on the extremely constrained model of passive communication, which assumes that when observing another agent the only information that can be extracted is the opinion bit of that agent. We prove that this problem can be solved in a poly-logarithmic in n number of rounds with high probability, while sampling a logarithmic number of agents at each round. Previous works solved this problem faster and using fewer samples, but they did that by decoupling the messages sent by agents from their output opinion, and hence do not fit the framework of passive communication. Moreover, these works use complex recursive algorithms with refined clocks that are unlikely to be used by biological entities. In contrast, our proposed algorithm has a natural appeal as it is based on letting agents estimate the current tendency direction of the dynamics, and then adapt to the emerging trend.

如何在系统中高效可靠地传播信息是分布式计算中最基本的问题之一。最近，受生物场景的启发，一些工作重点关注确定在错误条件下传播信息所需的最小通信资源。在这里，我们研究Boczkowski、Korman 和 Natale 在 [SODA 2017] 中引入的自稳定位传播问题。该问题考虑了一个由n 个 代理组成的完全连接的网络，具有二元意见世界，其中之一称为正确的。在任何给定时间，每个代理都持有一个意见位作为其公共输出。群体中包含一个知道哪种观点是正确的源代理。该代理人采纳正确的意见并在整个执行过程中坚持下去。我们考虑基本的\(\mathcal {PULL}\)通信模型，其中每个智能体在每轮中观察相对较少的随机选择的智能体。非源代理的目标是快速收敛于正确的意见，尽管具有任意的初始配置，即以自稳定的方式。一旦人们一致同意正确的观点，它就应该永远保留下去。受动物观察他人行为并对其做出反应的生物场景的启发，我们专注于被动通信的极其受限的模型，该模型假设在观察另一个代理时，唯一可以提取的信息是该代理的意见位。我们证明这个问题可以在 n轮中以高概率以多对数方式解决，同时在每轮对对数数量的代理进行采样。以前的工作更快地解决了这个问题，并且使用了更少的样本，但是他们通过将代理发送的消息与其输出意见解耦来实现这一点，因此不适合被动通信的框架。此外，这些作品使用复杂的递归算法和精确的时钟，而生物实体不太可能使用这些时钟。相比之下，我们提出的算法具有天然的吸引力，因为它基于让智能体估计动态的当前趋势方向，然后适应新出现的趋势。