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Stabilizing Consensus Is Impossible in Lossy Iterated Immediate Snapshot Models

Authors Stephan Felber , Hugo Rincon Galeana

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Author Details

Stephan Felber
  • Vienna University of Technology, Austria
Hugo Rincon Galeana
  • Vienna University of Technology, Austria
  • Berlin University of Technology, Germany

Funding

This work was supported by the DMAC project (P32431).
  • Rincon Galeana, Hugo: supported by German Research Foundation (DFG), Schwerpunktprogramm (SPP 2378), project ReNO, 2023-2027, and the financial support of Najla Amira Ochoa Leonor.

Acknowledgements

We would like to thank Ulrich Schmid and Kyrill Winkler for their helpful remarks, which undoubtedly improved this paper.

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Stephan Felber and Hugo Rincon Galeana. Stabilizing Consensus Is Impossible in Lossy Iterated Immediate Snapshot Models. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.18

Abstract

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.
Stabilizing consensus has been studied within the context of synchronous message adversaries. In particular, Charron-Bost and Moran showed that a necessary condition for stabilizing consensus is the existence of at least one process that reaches all others infinitely often (a perpetual broadcaster). However, it was left open whether this is also a sufficient condition for solving stabilizing consensus.
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.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Fault-tolerant network topologies
  • Networks → Network properties
  • Theory of computation → Distributed algorithms
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • distributed systems
  • dynamic networks
  • dynamic graphs
  • message adversaries
  • stabilizing consensus
  • asynchronous message passing

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