Unifying Partial Synchrony

TL;DR

The paper addresses the practical question of whether the GST and UL partially synchronous models are equally expressive for time-agnostic properties. It introduces a clock-slowing reduction that simulates GST behavior within the UL model by wrapping the global clock with $\textsc{SlowClock}(t)=\sqrt{t}$, ensuring that the observed network delay eventually falls below any fixed bound. The authors prove that if a protocol $\Pi$ achieves a time-agnostic property $X$ in GST$(1,\textsc{RealClock})$, then there exists a constructed protocol $\Pi'$ that achieves the same property $X$ in UL$(\Delta,\textsc{RealClock})$ for all $\Delta\ge 0$, under mild assumptions about clocks and adversaries. This result formalizes and generalizes the intuition that GST and UL are equally demanding for time-agnostic properties, clarifying model interchanges and enabling transfer of correctness results across these partially synchronous settings. The work has implications for designing robust distributed protocols in environments with transient delays, showing that GST-based analyses suffice to guarantee properties in UL, provided the wrapper-based slowdown is employed.

Abstract

The distributed computing literature considers multiple options for modeling communication. Most simply, communication is categorized as either synchronous or asynchronous. Synchronous communication assumes that messages get delivered within a publicly known timeframe and that parties' clocks are synchronized. Asynchronous communication, on the other hand, only assumes that messages get delivered eventually. A more nuanced approach, or a middle ground between the two extremes, is given by the partially synchronous model, which is arguably the most realistic option. This model comes in two commonly considered flavors: (i) The Global Stabilization Time (GST) model: after an (unknown) amount of time, the network becomes synchronous. This captures scenarios where network issues are transient. (ii) The Unknown Latency (UL) model: the network is, in fact, synchronous, but the message delay bound is unknown. This work formally establishes that any time-agnostic property that can be achieved by a protocol in the UL model can also be achieved by a (possibly different) protocol in the GST model. By time-agnostic, we mean properties that can depend on the order in which events happen but not on time as measured by the parties. Most properties considered in distributed computing are time-agnostic. The converse was already known, even without the time-agnostic requirement, so our result shows that the two network conditions are, under one sensible assumption, equally demanding.

Theorems & Definitions (6)

• Theorem 1
• Lemma 2
• proof
• Lemma 3
• proof
• proof : Proof of Theorem \ref{['thm:main']}