The Topology of Asynchronous Byzantine Colorless Tasks

In this paper, we extend the topological model that characterizes task solvability in crash-failure systems to colorless tasks in Byzantine asynchronous systems. We give the first theorem with necessary and sufficient conditions to solve arbitrary colorless tasks in such model, capturing the relation between the total number of processes, the number of faulty processes, and the topological structure of he task's simplicial complexes. In the interim, we provide novel asynchronous protocols for k-set agreement and barycentric agreement with optimal Byzantine fault tolerance.