# Population protocols with unreliable communication

## TL;DR

This paper investigates how unreliable communication affects the computational power of population protocols, showing that many models become less expressive under message loss, with immediate observation protocols remaining robust.

## Contribution

It demonstrates that unreliable communication limits the expressive power of population protocols, establishing that many models are equivalent to immediate observation protocols in such settings.

## Key findings

- Unreliable protocols with constant storage can only compute predicates of immediate observation protocols.
- Immediate observation protocols are inherently tolerant of unreliable communication.
- Many more expressive message-based models become less expressive under message loss.

## Abstract

Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities occur nondeterministically, allowing the agents involved to change their states based on each other's states. In the present paper we study unreliable models based on population protocols and their variations from the point of view of expressive power. We model the effects of message loss. We show that for a general definition of unreliable protocols with constant-storage agents such protocols can only compute predicates computable by immediate observation population protocols (sometimes also called one-way protocols). Immediate observation population protocols are inherently tolerant of unreliable communication and keep their expressive power under a wide range of fairness conditions. We also prove that a large class of message-based models that are generally more expressive than immediate observation becomes strictly less expressive than immediate observation in the unreliable case.