Tuesday 6.4.2021, 11:00, online

**Abstract:** 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 independent interest called the
sequential flow problem, and study the complexity of solving it.