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Optimally Controlling a Random Population

Authors Hugo Gimbert , Corto Mascle , Patrick Totzke

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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Controller synthesis
  • Parameterized verification

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Abstract

The population control problem is a parameterised problem where a controller sends messages to a whole population of identical finite-state agents, aiming to eventually move them all into a target state. The decision problem asks whether this can be achieved for arbitrarily large finite populations. We focus on the randomised version of this problem, where every agent is a copy of the same finite Markov Decision Process and non-determinism in the global action chosen by the controller is resolved independently and uniformly at random. Colcombet, Fijalkow and Ohlmann [Thomas Colcombet et al., 2021] showed that this problem is decidable, but without any complexity upper bound. We show that the random population control problem is in fact ExpTime-complete.

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Hugo Gimbert, Corto Mascle, and Patrick Totzke. Optimally Controlling a Random Population. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 180:1-180:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.180

Author Details

Hugo Gimbert
  • CNRS, LaBRI, Université de Bordeaux, Talence, France
Corto Mascle
  • Max Planck Institute for Software Systems, Kaiserslautern, Germany
Patrick Totzke
  • University of Liverpool, UK

Funding

  • Totzke, Patrick: EPSRC, grant no.: EP/X042596/1.

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