A characterization of colorless anonymous $t$-resilient task computability

Abstract

A task is a distributed problem for n processes, in which each process starts with a private input value, communicates with other processes, and eventually decides an output value. A task is colorless if each process can adopt the input or output value of another process. Colorless tasks are well studied in the non-anonymous sharedmemory model where each process has a distinct identifier that can be used to access a single-writer/multi-reader shared register. In the anonymous case, where processes have no identifiers and communicate through multiwriter/multi-reader registers, there is a recent topological characterization of the colorless tasks that are solvable when any number of asynchronous processes may crash.In this paper we study the case where at most t processes may crash, where 1 ≤ t < n. We prove that a colorless task is t-resilient solvable non-anonymously if and only if it is t-resilient solvable anonymously. This implies a complete characterization of colorless anonymous t-resilient asynchronous task computability.