Population protocols form a well-established model of computation of passively mobile anonymous agents with constant-size memory. It is well known that population protocols compute Presburger-definable predicates, such as absolute majority and counting predicates. In this work, we initiate the study of population protocols operating over arbitrarily large data domains. More precisely, we introduce population protocols with unordered data as a formalism to reason about anonymous crowd computing over unordered sequences of data. We first show that it is possible to determine whether an unordered sequence from an infinite data domain has a datum with absolute majority. We then establish the expressive power of the immediate observation restriction of our model, namely where, in each interaction, an agent observes another agent who is unaware of the interaction.

翻译：种群协议是一种成熟的被动移动匿名代理计算模型，其内存大小恒定。众所周知，种群协议可计算Presburger可定义谓词，例如绝对多数和计数谓词。本文首次研究了在任意大数据域上运行的种群协议。具体而言，我们引入了无序数据上的种群协议，作为一种形式化方法，用于推理针对无序数据序列的匿名众包计算。我们首先证明，能够判定来自无限数据域的无序序列中是否存在具有绝对多数的数据项。接着，我们确立了该模型在即时观察限制下的表达能力，即在每次交互中，一个代理观察另一个未察觉该交互的代理时的表达能力。