The computational power of population protocols

TL;DR

This paper characterizes the computational power of population protocols, proving they can stably compute exactly the semilinear predicates, and explores variants with one-way communication, identifying their computational limits.

Contribution

It establishes that all predicates stably computable in the population protocol model are semilinear, and extends the analysis to one-way communication variants with detailed predicate classifications.

Findings

All stably computable predicates are semilinear.

One-way communication models have distinct classes of computable predicates.

Characterization of predicate classes in various communication models.

Abstract

We consider the model of population protocols introduced by Angluin et al., in which anonymous finite-state agents stably compute a predicate of the multiset of their inputs via two-way interactions in the all-pairs family of communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power of the model. Removing the assumption of two-way interaction, we also consider several variants of the model in which agents communicate by anonymous message-passing where the recipient of each message is chosen by an adversary and the sender is not identified to the recipient. These one-way models are distinguished by whether messages are delivered immediately or after a delay, whether a sender can record that it has sent a message, and whether a recipient can queue incoming messages, refusing to accept new messages until it has had a chance to send out messages of its own. We characterize the classes of predicates stably computable in each of these one-way models using natural subclasses of the semilinear predicates.