Distributed Computability in Byzantine Asynchronous Systems

TL;DR

This paper extends topology-based methods to characterize what can be computed in asynchronous Byzantine systems, providing necessary and sufficient conditions for solving arbitrary distributed tasks under adversarial faults.

Contribution

It introduces the first theorem with necessary and sufficient conditions for task solvability in asynchronous Byzantine systems using a topology-based approach.

Findings

Provides a comprehensive topological characterization of Byzantine computability.

Reduces to an elegant model for colorless tasks relating processes, failures, and topology.

Establishes fundamental limits for distributed computing in Byzantine environments.

Abstract

In this work, we extend the topology-based approach for characterizing computability in asynchronous crash-failure distributed systems to asynchronous Byzantine systems. We give the first theorem with necessary and sufficient conditions to solve arbitrary tasks in asynchronous Byzantine systems where an adversary chooses faulty processes. In our adversarial formulation, outputs of non-faulty processes are constrained in terms of inputs of non-faulty processes only. For colorless tasks, an important subclass of distributed problems, the general result reduces to an elegant model that effectively captures the relation between the number of processes, the number of failures, as well as the topological structure of the task's simplicial complexes.