[KNP19] Marta Kwiatkowska, Gethin Norman and David Parker. Verification and Control of Turn-Based Probabilistic Real-Time Games. In The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy (Essays Dedicated to Catuscia Palamidessi on the Occasion of Her 60th Birthday), volume 11760 of LNCS, pages 379-396, Springer. November 2019. [pdf] [bib] [Proposes techniques for verifying probabilistic real-time games building on methods implemented in PRISM-games.]
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Notes: Supporting material available at http://www.prismmodelchecker.org/files/tptgs/. The original publication is available at link.springer.com.
Abstract. 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.