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.

翻译：分布式计算研究的相当一部分致力于终止性问题，如共识及类似的协议问题。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，并能容忍任意的瞬时故障。介于两者之间的是稳定化问题，其中进程从明确定义的初始状态开始，但无需不可撤销地做出决定，并且允许在最终达到稳定决策之前有限次地更改其决定。本文引入了新颖的延迟损失链路模型以及损失性迭代即时快照模型，并证明了在这些模型中稳定共识是不可能的。延迟损失链路模型作为众所周知的损失链路模型的变体被引入，该模型允许任意但有限长度的静默期。损失性迭代即时快照模型是迭代即时快照模型的变体，该模型允许每层最多发生$f$次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，即使在连接性极强的模型——即迭代即时快照模型中，每层仅发生一次遗漏故障就足以使稳定共识无法实现。此外，由于延迟损失链路模型始终存在一个永久广播者，即使在无崩溃的环境中，仅存在永久广播者也不足以解决稳定共识问题，这从负面回答了Charron-Bost和Moran提出的开放性问题。