Verification and Control of Turn-Based Probabilistic Real-Time Games

  • Marta Kwiatkowska
  • Gethin NormanEmail author
  • David Parker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11760)


Quantitative verification techniques have been developed for the formal analysis of a variety of probabilistic models, such as Markov chains, Markov decision process and their variants. They can be used to produce guarantees on quantitative aspects of system behaviour, for example safety, reliability and performance, or to help synthesise controllers that ensure such guarantees are met. We propose the model of turn-based probabilistic timed multi-player games, which incorporates probabilistic choice, real-time clocks and nondeterministic behaviour across multiple players. Building on the digital clocks approach for the simpler model of probabilistic timed automata, we show how to compute the key measures that underlie quantitative verification, namely the probability and expected cumulative price to reach a target. We illustrate this on case studies from computer security and task scheduling.



This work is partially supported by the EPSRC Programme Grant on Mobile Autonomy and the PRINCESS project, under the DARPA BRASS programme (contract FA8750-16-C-0045).


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Authors and Affiliations

  1. 1.Department of Computing ScienceUniversity of OxfordOxfordUK
  2. 2.School of Computing ScienceUniversity of GlasgowGlasgowUK
  3. 3.School of Computer ScienceUniversity of BirminghamBirminghamUK

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