Asynchrony from Synchrony

TL;DR

This paper characterizes the minimal message survivability needed in synchronous dynamic networks with asymmetric links to solve wait-free read-write tasks, identifying a strongest adversary that matches read-write solvability.

Contribution

It provides a complete characterization of message adversaries that enable solving any wait-free read-write task, simplifying the proof of protocol complex properties.

Findings

Identifies a strongest message adversary for wait-free read-write tasks.

Shows this adversary matches the power of processor failure models like ABD.

Simplifies the topological proof of task solvability in dynamic networks.

Abstract

We consider synchronous dynamic networks which like radio networks may have asymmetric communication links, and are affected by communication rather than processor failures. In this paper we investigate the minimal message survivability in a per round basis that allows for the minimal global cooperation, i.e., allows to solve any task that is wait-free read-write solvable. The paper completely characterizes this survivability requirement. Message survivability is formalized by considering adversaries that have a limited power to remove messages in a round. Removal of a message on a link in one direction does not necessarily imply the removal of the message on that link in the other direction. Surprisingly there exist a single strongest adversary which solves any wait-free read/write task. Any different adversary that solves any wait-free read/write task is weaker, and any stronger adversary will not solve any wait-free read/write task. ABD \cite{ABD} who considered processor failure, arrived at an adversary that is $n/2$ resilient, consequently can solve tasks, such as $n/2$-set-consensus, which are not read/write wait-free solvable. With message adversaries, we arrive at an adversary which has exactly the read-write wait-free power. Furthermore, this adversary allows for a considerably simpler (simplest that we know of) proof that the protocol complex of any read/write wait-free task is a subdivided simplex, finally making this proof accessible for students with no algebraic-topology prerequisites, and alternatively dispensing with the assumption that the Immediate Snapshot complex is a subdivided simplex.