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

TL;DR

This paper proves that for colorless tasks, the set of tasks solvable with up to t crashes is the same in both anonymous and non-anonymous models, providing a complete characterization of their computability.

Contribution

It establishes that t-resilient solvability of colorless tasks is equivalent in anonymous and non-anonymous models, extending topological characterizations to the anonymous setting.

Findings

t-resilient solvability is equivalent in both models

Complete topological characterization for anonymous tasks

Extension of non-anonymous results to anonymous setting

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 shared-memory 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 multi-writer/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 $1 \le t < n$. 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.