在有损迭代即时快照模型中稳定共识是不可能的
Stabilizing Consensus is Impossible in Lossy Iterated Immediate Snapshot Models
AI总结：
本文提出了DLL和LIIS模型，证明了即使在每层仅存在1个遗漏故障的强连接IIS模型中稳定共识也无法实现，并指出仅存在永久广播者不足以解决稳定共识。
摘要：
分布式计算研究的很大一部分致力于共识及类似一致性问题等终止性问题。然而，非终止性问题在自稳定分布式算法的背景下得到了深入研究，其中进程可以从任意初始状态开始，并且能够容忍任意瞬态故障。介于两者之间的是稳定问题，进程从明确定义的初始状态开始，但不需要不可撤销地做出决定，并允许有限次地改变其决定，直到最终达到稳定的决定。在本文中，我们引入了新颖的 Delayed Lossy-Link (DLL) 模型和 Lossy Iterated Immediate Snapshot Model (LIIS) 模型，并证明了在这两个模型中稳定共识是不可能的。DLL 模型作为著名的 Lossy-Link 模型的变体被引入，它允许任意但有限长度的静默期。LIIS 模型是 Iterated Immediate Snapshot (IIS) 模型的变体，允许每层最多 $f$ 个遗漏故障的有限长度周期。特别地，我们证明了即使当 $f=1$ 时，稳定共识也是不可能的。我们的结果表明，即使在一个具有非常强连接性的模型中，即 Iterated Immediate Snapshot (IIS) 模型，每层单个遗漏故障也会有效地使稳定共识失效。此外，由于 DLL 模型总是有一个永久的广播者，因此仅仅存在一个永久的广播者，即使在无崩溃的设置中，也不足以解决稳定共识，这否定地回答了 Charron-Bost 和 Moran 提出的开放问题。
英文摘要：
A substantial portion of distributed computing research is dedicated to terminating problems like consensus and similar agreement problems. However, non-terminating problems have been intensively studied in the context of self-stabilizing distributed algorithms, where processes may start from arbitrary initial states and can tolerate arbitrary transient faults. In between lie stabilizing problems, where the processes start from a well-defined initial state, but do not need to decide irrevocably and are allowed to change their decision finitely often until a stable decision is eventually reached. In this paper, we introduce the novel Delayed Lossy-Link (DLL) model, and the Lossy Iterated Immediate Snapshot Model (LIIS), for which we show stabilizing consensus to be impossible. The DLL model is introduced as a variant of the well-known Lossy-Link model, which admits silence periods of arbitrary but finite length. The LIIS model is a variant of the Iterated Immediate Snapshot (IIS), model which admits finite length periods of at most $f$ omission faults per layer. In particular, we show that stabilizing consensus is impossible even when $f=1$. Our results show that even in a model with very strong connectivity, namely, the Iterated Immediate Snapshot (IIS) model, a single omission fault per layer effectively disables stabilizing consensus. Furthermore, since the DLL model always has a perpetual broadcaster, the mere existence of a perpetual broadcaster, even in a crash-free setting, is not sufficient for solving stabilizing consensus, negatively answering the open question posed by Charron-Bost and Moran.
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