Given a boolean predicate on labeled networks (e.g., the network is acyclic, or the network is properly colored, etc.), deciding in a distributed manner whether a given labeled network satisfies that predicate typically consists, in the standard setting, of every node inspecting its close neighborhood, and outputting a boolean verdict, such that the network satisfies the predicate if and only if all nodes output true. In this paper, we investigate a more general notion of distributed decision in which every node is allowed to output a constant number $$b\ge 1$$ b ≥ 1 of bits, which are gathered by a central authority emitting a global boolean verdict based on these outputs, such that the network satisfies the predicate if and only if this global verdict equals true. We analyze the power and limitations of this extended notion of distributed decision.

中文翻译：

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使用少量输出位在本地确定和验证网络属性

给定标记网络上的布尔谓词（例如，网络是非循环的，或者网络具有适当的颜色等），以分布式方式决定给定的标记网络是否满足该谓词在标准设置中通常由每个节点组成检查它的近邻，并输出一个布尔判断，这样当且仅当所有节点都输出真时，网络才满足谓词。在本文中，我们研究了一个更一般的分布式决策概念，其中允许每个节点输出一个常数 $$b\ge 1$$ b ≥ 1 位，这些位由中央机构收集，发出全局布尔判定基于这些输出，当且仅当这个全局判断等于真时，网络才满足谓词。