Stabilizing Consensus is Impossible in Lossy Iterated Immediate Snapshot Models
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917834093756416 |
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| author | Felber, Stephan Galeana, Hugo Rincon |
| author_facet | Felber, Stephan Galeana, Hugo Rincon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilizing Consensus is Impossible in Lossy Iterated Immediate Snapshot Models Felber, Stephan Galeana, Hugo Rincon Distributed, Parallel, and Cluster Computing C.2.4; F.2.0; G.2.2 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. |
| title | Stabilizing Consensus is Impossible in Lossy Iterated Immediate Snapshot Models |
| topic | Distributed, Parallel, and Cluster Computing C.2.4; F.2.0; G.2.2 |
| url | https://arxiv.org/abs/2402.09168 |