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

@article{paperbot1264,
  title = {Controlling a random population},
  author = {Thomas Colcombet and Nathanaël Fijalkow and Pierre Ohlmann},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 17, Issue 4},
  year = {2021},
  doi = {10.46298/lmcs-17(4:12)2021}
}