Controlling a random population

Bertrand et al. introduced a model of parameterised systems, where each agent is represented by finite state system, and studied the following control problem: for any number agents, does there exist controller able to bring all agents target state? They showed that problem decidable EXPTIME-complete in adversarial setting, posed as an open stochastic Markov decision process. In this paper, we show decidable. Our solution makes significant uses well quasi orders, max-flow min-cut theorem, theory regular cost functions. We introduce intermediate independence interest called sequential flow study its complexity.