Symmetry all the way down

2026-07-06

AI Summary

This work investigates whether asymmetric trust models enhance the solvability of distributed tasks of depth two or higher, such as consensus and reliable broadcast. Through a hierarchical analysis based on task depth and the construction of formal compilers, the study establishes—for the first time—that while asymmetric trust broadens the set of tolerable failure scenarios, it confers no additional solvability advantage for tasks of depth ≥ 2 compared to symmetric trust models; their solvability remains equivalent. Only tasks of depth ≤ 1, such as consistent broadcast, benefit from asymmetry. This result is tight within the depth hierarchy, precisely delineating the expressive power and inherent limitations of asymmetric trust in distributed computing.

Abstract

Asymmetric trust generalizes classical symmetric quorum systems by allowing each process to specify its own failure assumptions. While this flexibility enables tolerance of strictly more failure scenarios, it is not known if, in these cases, it is actually possible to solve distributed tasks, and if so, which. We answer this question using the depth hierarchy for asymmetric trust (Amores-Sesar et al., OPODIS~'25), which characterizes how much a process must rely on others to solve a task. We prove that asymmetric trust does not increase the solvability of tasks requiring depth two or more, such as reliable broadcast or consensus. Specifically, for any Byzantine asymmetric quorum system, every failure scenario that permits solving a task requiring depth at least two can also be tolerated by a suitably constructed Byzantine symmetric quorum system. We show this via a compiler that transforms asymmetric quorum systems into symmetric ones. The additional failure patterns tolerated exclusively by asymmetric trust correspond to scenarios in which only simpler tasks requiring depth one or less (such as consistent broadcast) can be solved. We further prove that this result is tight in the depth hierarchy, meaning that there exist no compilers that produce symmetric quorum systems that are valid also in failure scenarios where correct processes have depths one or less. Our results clarify the precise power of asymmetric trust. While it strictly enlarges the set of tolerable failure patterns, it does not provide additional strength for solving tasks requiring depth two or higher.

Problem

• asymmetric trust
• distributed tasks
• quorum systems
• fault tolerance
• depth hierarchy

Innovation

• asymmetric trust
• quorum systems
• depth hierarchy
• distributed consensus
• Byzantine fault tolerance