Most distributed computing research has focused on terminating problems like consensus and similar agreement problems. Non-terminating problems have been studied exhaustively in the context of self-stabilizing distributed algorithms, however, which may start from arbitrary initial states and can tolerate arbitrary transient faults. Somehow in-between is the stabilizing consensus problem, where the processes start from a well-defined initial state but do not need to decide irrevocably and need to agree on a common value only eventually. Charron-Bost and Moran studied stabilizing consensus in synchronous dynamic networks controlled by a message adversary. They introduced the simple and elegant class of min-max algorithms, which allow to solve stabilizing consensus under every message adversary that (i) allows at least one process to reach all other processes infinitely often, and (ii) does so within a bounded (but unknown) number of rounds. Moreover, the authors proved that (i) is a necessary condition. The question whether (i) is also sufficient, i.e., whether (ii) is also necessary, was left open. We answer this question by proving that stabilizing consensus is impossible if (ii) is dropped, i.e., even if some process reaches all other processes infinitely often but only within finite time. We accomplish this by introducing a novel class of arbitrarily delayed message adversaries, which also allows us to establish a connection between terminating task solvability under some message adversary to stabilizing task solvability under the corresponding arbitrarily delayed message adversary. Finally, we outline how to extend this relation to terminating task solvability in asynchronous message passing with guaranteed broadcasts, which highlights the asynchronous characteristics induced by arbitrary delays.

翻译：大多数分布式计算研究聚焦于终止性问题，如共识及类似一致性问题。然而，自稳定分布式算法领域已对非终止性问题进行了详尽研究，此类算法可从任意初始状态启动并容忍任意瞬时故障。介于两者之间的是稳定性一致问题，其中进程从明确初始状态启动，但无需做出不可撤销的决策，仅需最终就某个公共值达成一致。Charron-Bost 与 Moran 研究了由消息对手控制的同步动态网络中的稳定性一致问题。他们提出了简洁优雅的极大极小算法类，此类算法可在满足以下条件的任意消息对手下解决稳定性一致：(i) 至少允许一个进程无限频繁地到达所有其他进程；(ii) 且该过程在有限（但未知）轮次内完成。此外，作者证明了条件 (i) 是必要条件。然而，条件 (i) 是否充分（即条件 (ii) 是否也为必要）的问题仍未解决。我们通过证明若移除条件 (ii)（即即使某个进程在有限时间内无限频繁地到达所有其他进程），稳定性一致仍不可能实现，从而解答了该问题。为此，我们引入了一类新型的任意延迟消息对手，该模型还使我们能够建立某些消息对手下终止性任务可解性与对应任意延迟消息对手下稳定性任务可解性之间的联系。最后，我们概述了如何将此关系扩展到具有保证广播的异步消息传递中的终止性任务可解性，这突出了由任意延迟引发的异步特性。