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Strategy Synthesis for Global Window PCTL

Authors Benjamin Bordais, Damien Busatto-Gaston , Shibashis Guha , Jean-François Raskin

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Benjamin Bordais
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, 91190 Gif-sur-Yvette, France
Damien Busatto-Gaston
  • Université libre de Bruxelles, Brussels, Belgium
Shibashis Guha
  • Tata Institute of Fundamental Research, Mumbai, India
Jean-François Raskin
  • Université libre de Bruxelles, Brussels, Belgium

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Benjamin Bordais, Damien Busatto-Gaston, Shibashis Guha, and Jean-François Raskin. Strategy Synthesis for Global Window PCTL. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 115:1-115:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Given a Markov decision process (MDP) M and a formula Φ, the strategy synthesis problem asks if there exists a strategy σ s.t. the resulting Markov chain M[σ] satisfies Φ. This problem is known to be undecidable for the probabilistic temporal logic PCTL. We study a class of formulae that can be seen as a fragment of PCTL where a local, bounded horizon property is enforced all along an execution. Moreover, we allow for linear expressions in the probabilistic inequalities. This logic is at the frontier of decidability, depending on the type of strategies considered. In particular, strategy synthesis is decidable when strategies are deterministic while the general problem is undecidable.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Stochastic processes
  • Markov decision processes
  • synthesis
  • PCTL


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