Stabilizing Consensus is Impossible in Lossy Iterated Immediate Snapshot Models

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. 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.

• The paper proves that stabilizing consensus is impossible in systems with lossy iterated immediate snapshots, highlighting the effect of unbounded message delays.
• It introduces a novel class of delayed message adversaries that formalize the challenges in achieving agreement, contrasting bounded delay conditions with scenarios of indefinite message silences.
• The study extends classic asynchronous impossibility results, underscoring the need for redesigned distributed consensus protocols in unreliable, dynamic networks.

Stabilizing Consensus in Lossy Iterated Immediate Snapshot Models

Introduction

The paper "Stabilizing Consensus is Impossible in Lossy Iterated Immediate Snapshot Models" (2402.09168) investigates the dynamic capabilities and limitations of achieving stabilizing consensus in distributed systems. The focus is on systems modeled through lossy iterated immediate snapshot behaviors, which are foundational in distributed computing for addressing consensus and agreement problems in asynchronous message-passing environments. The paper provides critical insights into the impossibility of establishing stabilizing consensus within specific protocol settings postulated by previous research by Charron-Bost and others.

Background and Motivation

Consensus is a fundamental problem in distributed systems, wherein processes must agree on a single data value despite failures and varying initial states. Conventional approaches mainly address terminating problems by ensuring every correct process eventually decides on the same value. However, stabilizing consensus, where processes start from well-defined states but do not irrevocably decide, introduces persistent agreement over iterative snapshots.

Prior work by Charron-Bost and Moran proposed conditions under which stabilizing consensus could be achieved using min-max algorithms within synchronous dynamic networks controlled by message adversaries. Their research suggested that allowing a process to infinitely often reach all others with bounded rounds could solve stabilizing consensus. This paper challenges and extends that proposition, examining the sufficiency of these conditions when some synchronization assumptions are relaxed through lossy links.

Main Contributions

Impossibility of Stabilizing Consensus

The paper conclusively demonstrates that stabilizing consensus is impossible in iterated immediate snapshot models where messages suffer arbitrary delays. A central assumption examined is whether having a single process that reaches all others infinitely often ensures stabilizing consensus. The authors introduce a novel class of message adversaries, delineating that bounded but unknown delay conditions are crucial, and without such bounds, achieving consensus amidst constant changes and delays becomes unmanageable.

Delayed and Lossy Message Models

By contrasting models with bounded delays against message-passing scenarios allowing indefinite silences, the research establishes a connection between stabilizing consensus under varying adversary controls and conventional task solvability. The findings underscore how delays and losses in message propagation create scenarios of unresolvable uncertainty in decision making, rendering stabilizing consensus unsolvable even with perpetual broadcasters.

Asynchronous Message Passing

An extension of the problem to asynchronous environments highlights how the uncertainty induced by arbitrary delays equalizes disparate models into asynchronous equivalences. This result extends familiar impossibility results, such as those by Fischer, Lynch, and Paterson (FLP), historically reliant on such asynchronous characteristics for proving consensus intractability.

Theoretical and Practical Implications

This research has significant implications for the theory and practice of distributed computing. It offers a theoretical underpinning for understanding the limitations of consensus protocols in dynamic and asynchronous settings subjected to imperfect communication channels. Practically, it calls for reconsideration in designing distributed algorithms, particularly those reliant on network assumptions about message propagation and round-based consensus mechanisms.

Furthermore, it opens pathways for reevaluating consensus models and their adaptation to environments plagued by faults and communication uncertainties. Future work could explore more robust approaches that incorporate richer failure detectors and adaptive protocol strategies supportive of continuous task recalibration, particularly in sensor networks and decentralizing computing systems.

Conclusion

The paper robustly argues against the feasibility of stabilizing consensus in lossy iterated immediate snapshot models by introducing critical insights into delayed message adversaries and asynchronous extensions. It redefines achievable bounds within distributed consensus protocols, advocating for revised strategies in algorithm designs and network models accounting for unavoidable message loss and delay. This research enriches the ongoing discourse on consensus by establishing foundational impossibility results and by benchmarking conditions under which dynamic distributed agreement tasks are inherently constrained.