January 27, 2020

Pierre Ohlmann (IRIF)

Bertrand et al. (2017) 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.