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

2025-11-26

AI Summary

This paper investigates the equivalence and separation between the asynchronous message-passing model and the Heard-Of (HO) model in distributed computing, focusing on solvability relations for colorless and colored tasks under crash and message-omission fault models. Using bidirectional simulation, it introduces an intermediate model to capture silent process behavior in omission failures and extends the analysis to randomized protocols and non-adaptive adversaries. The main contributions are threefold: (1) a rigorous proof that the two models are fully equivalent for colorless tasks; (2) a demonstration that they are equivalent for colored tasks only when the fault tolerance bound $ f = 1 $, with silent processes identified— for the first time—as the fundamental cause of decision conflicts leading to separation; and (3) a precise characterization of the necessary and sufficient conditions under which the round-based abstraction of the HO model exactly captures asynchronous computability, thereby providing a structural understanding of model relationships in distributed computing.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Compares equivalence of asynchronous message-passing and Heard-Of models for colorless tasks
• Shows separation for colored tasks due to silenced processes causing incompatible decisions
• Extends results to randomized protocols against non-adaptive adversaries

Innovation

• Bidirectional simulations between AMP_f and HO_f
• Intermediate model capturing silencing notion
• Equivalence for colorless tasks when n > 2f