Equivalence and Separation between Heard-Of and Asynchronous Message-Passing Models

TL;DR

This paper analyzes the relationship between asynchronous message-passing and Heard-Of models, establishing conditions for their equivalence in solving distributed tasks and highlighting the impact of silenced processes on their separation.

Contribution

It provides a detailed characterization of when these two fundamental models are equivalent or separated, introducing an intermediate model to explain the differences.

Findings

Models are equivalent for colorless tasks when n > 2f.

Equivalence for colored tasks only when f=1 and n > 2.

Silenced processes cause separation for larger f.

Abstract

We revisit the relationship between two fundamental models of distributed computation: the asynchronous message-passing model with up to $f$ crash failures ($\operatorname{AMP}_f$) and the Heard-Of model with up to $f$ message omissions ($\operatorname{HO}_f$). We show that for $n > 2f$, the two models are equivalent with respect to the solvability of colorless tasks, and that for colored tasks the equivalence holds only when $f = 1$ (and $n > 2$). The separation for larger $f$ arises from the presence of silenced processes in $\operatorname{HO}_f$, which may lead to incompatible decisions. The proofs proceed through bidirectional simulations between $\operatorname{AMP}_f$ and $\operatorname{HO}_f$ via an intermediate model that captures this notion of silencing. The results extend to randomized protocols against a non-adaptive adversary, indicating that the expressive limits of canonical rounds are structural rather than probabilistic. Together, these results delineate precisely where round-based abstractions capture asynchronous computation, and where they do not.