Thomas Colcombet ; Nathanaël Fijalkow ; Pierre Ohlmann - Controlling a random population

lmcs:7034 - Logical Methods in Computer Science, November 24, 2021, Volume 17, Issue 4 - https://doi.org/10.46298/lmcs-17(4:12)2021
Controlling a random population

Authors: Thomas Colcombet ; Nathanaël Fijalkow ; Pierre Ohlmann

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.


Volume: Volume 17, Issue 4
Published on: November 24, 2021
Accepted on: September 28, 2021
Submitted on: January 1, 2021
Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Distributed, Parallel, and Cluster Computing,Computer Science - Computer Science and Game Theory,Computer Science - Logic in Computer Science


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