# Expressive Power of Broadcast Consensus Protocols

## TL;DR

This paper demonstrates that extending population protocols with reliable broadcast capabilities enhances their computational power to match the class NL, simplifying implementation compared to previous complex extensions.

## Contribution

The paper introduces reliable broadcast as a simpler extension to population protocols, achieving NL-level computational power without complex device requirements.

## Key findings

- Reliable broadcast extends population protocols to NL power.
- Simpler implementation compared to previous extensions.
- Achieves computational power equivalent to NL class.

## Abstract

Population protocols are a formal model of computation by identical, anonymous mobile agents interacting in pairs. Their computational power is rather limited: Angluin et al. have shown that they can only compute the predicates over $\mathbb{N}^k$ expressible in Presburger arithmetic. For this reason, several extensions of the model have been proposed, including the addition of devices called cover-time services, absence detectors, and clocks. All these extensions increase the expressive power to the class of predicates over $\mathbb{N}^k$ lying in the complexity class NL when the input is given in unary. However, these devices are difficult to implement, since they require that an agent atomically receives messages from all other agents in a population of unknown size; moreover, the agent must know that they have all been received. Inspired by the work of the verification community on Emerson and Namjoshi's broadcast protocols, we show that NL-power is also achieved by extending population protocols with reliable broadcasts, a simpler, standard communication primitive.