In this paper we investigate the computational power of population protocols under some unreliable or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the context of population protocols, is the loss by one or both parties of the information transmitted in an interaction. The failure may or may not be detected by either party. In one-way models, on the other hand, communication happens only in one direction: only one of the two agents can change its state depending on both agents’ states, and the other agent may or may not be aware of the interaction. These notions can be combined, obtaining one-way protocols with (possibly detectable) omission failures. We start our investigation by providing a complete classification of all the possible models arising from the aforementioned weaknesses, and establishing the computational hierarchy of these models. We then address for each model the fundamental question of what additional power is necessary and sufficient to completely overcome the model’s weakness and make it able to simulate faultless two-way protocols; by “simulator” we mean a wrapper protocol that, implementing an atomic communication of states between two agents, converts any standard two-way protocol into one that works in a weaker model. We answer this question by presenting simulators that work under certain assumptions (e.g., additional memory, unique IDs, etc.) and by proving that simulation is impossible without such assumptions.

中文翻译：

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种群协议的容错模拟

在本文中，我们研究了在一些不可靠或较弱的交互模型下人口协议的计算能力。更准确地说，我们关注与交互能力相关的两个特征：遗漏失败和单向通信。遗漏失败是本文首次在人口协议的背景下引入的概念，是一方或双方在交互中传输的信息丢失。故障可能会或可能不会被任何一方检测到。另一方面，在单向模型中，通信仅发生在一个方向：两个代理中只有一个可以根据两个代理的状态改变其状态，另一个代理可能知道也可能不知道交互。这些概念可以结合起来，获得具有（可能可检测到的）遗漏失败的单向协议。我们通过提供由上述弱点引起的所有可能模型的完整分类并建立这些模型的计算层次结构来开始我们的调查。然后，我们为每个模型解决了一个基本问题，即需要和足够的额外功率才能完全克服模型的弱点并使其能够模拟无故障的双向协议；“模拟器”是指一种包装协议，它实现了两个代理之间的原子状态通信，将任何标准的双向协议转换为适用于较弱模型的协议。我们通过展示在某些假设（例如，额外的内存、唯一 ID 等）下工作的模拟器并证明没有这些假设就不可能进行模拟来回答这个问题。