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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Teoria Automatów


Controlling a random population

Prelegent: Pierre Ohlmann

2021-03-10 14:15

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.