Optimally Controlling a Random Population

Abstract: The population control problem is a parameterized control problem where a population of agents has to be moved simultaneously into a target state. The decision problem asks whether this can be achieved for a finite but arbitrarily large population. We focus on the random version of this problem, where every agent is a copy of the same automaton and non-determinism on the global action chosen by the controller is resolved independently and uniformly at random. Controller seeks to almost-surely gather the agents in the target states. We show that the random population control problem is exptime-complete.