Verifying Emergent Properties of Swarms

We investigate the general problem of establishing whether a swarm satisfies an emergent property. We put forward a formal model for swarms that accounts for their nature of unbounded collections of agents following simple local protocols. We formally define the decision problem of determining whether a swarm satisfies an emergent property. We introduce a sound and complete procedure for solving the problem. We illustrate the technique by applying it to the Beta aggregation algorithm.