Population Protocols with Faulty Interactions: the Impact of a Leader

TL;DR

This paper investigates how the presence of a leader influences the ability to simulate population protocols under weaker communication models with faults, providing a complete characterization and protocols for various scenarios.

Contribution

It offers a comprehensive analysis of leader-based simulation capabilities in faulty, one-way interaction models, including explicit protocols and impossibility proofs.

Findings

Simulation possible without omission faults with finite memory

Detectable omissions allow simulation with unbounded memory

Known bounds on omissions enable simulation except in specific one-way cases

Abstract

We consider the problem of simulating traditional population protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner's state during an interaction), which in turn may be detectable or undetectable. We focus on the impact of a leader, and we give a complete characterization of the models in which the presence of a unique leader in the system allows the construction of simulators: when simulations are possible, we give explicit protocols; when they are not, we give proofs of impossibility. Specifically, if each agent has only a finite amount of memory, the simulation is possible only if there are no omission faults. If agents have an unbounded amount of memory, the simulation is possible as long as omissions are detectable. If an upper bound on the number of omissions involving the leader is known, the simulation is always possible, except in the one-way model in which one side is unable to detect the interaction.