In the population protocol model, many problems cannot be solved in a self-stabilizing manner. However, global knowledge, such as the number of nodes in a network, sometimes enables the design of a self-stabilizing protocol for such problems. For example, it is known that we can solve the self-stabilizing leader election in complete graphs if and only if every node knows the exact number of nodes. In this article, we investigate the effect of global knowledge on the possibility of self-stabilizing population protocols in arbitrary graphs. Specifically, we clarify the solvability of the leader election problem, the ranking problem, the degree recognition problem, and the neighbor recognition problem by self-stabilizing population protocols with knowledge of the number of nodes and/or the number of edges in a network.

中文翻译：

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具有全球知识的自稳定人口协议

在种群协议模型中，很多问题无法以自稳的方式解决。但是，全局知识，例如网络中的节点数量，有时可以针对此类问题设计自稳定协议。例如，众所周知，当且仅当每个节点都知道节点的确切数量时，我们可以在完整图中解决自稳定领导者选举。在本文中，我们研究了全局知识对任意图中自稳定种群协议的可能性的影响。具体来说，我们通过了解网络中节点数和/或边数的自稳定种群协议来阐明领导者选举问题、排序问题、度识别问题和邻居识别问题的可解性。