[CFK+12] Taolue Chen, Vojtěch Forejt, Marta Kwiatkowska, David Parker and Aistis Simaitis. Automatic Verification of Competitive Stochastic Systems. In Proc. 18th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS'12), volume 7214 of LNCS, pages 315-330, Springer. March 2012. [pdf] [bib] [Introduces model checking techniques for stochastic multi-player games, implemented in the PRISM-games tool.]
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Notes: Please see [CFK+13b] for a journal version of this paper, including proofs as well as other extensions. Details of the models and properties presented in the paper are here. See also the accompanying tool PRISM-games. The original publication is available at link.springer.com.
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Abstract. We present automatic verification techniques for the modelling and analysis of probabilistic systems that incorporate competitive behaviour. These systems are modelled as turn-based stochastic multi-player games, in which the players can either collaborate or compete in order to achieve a particular goal. We define a temporal logic called rPATL for expressing quantitative properties of stochastic multi-player games. This logic allows us to reason about the collective ability of a set of players to achieve a goal relating to the probability of an event's occurrence or the expected amount of cost/reward accumulated. We give a model checking algorithm for verifying properties expressed in this logic and implement the techniques in a probabilistic model checker, based on the PRISM tool. We demonstrate the applicability and efficiency of our methods by deploying them to analyse and detect potential weaknesses in a variety of large case studies, including algorithms for energy management and collective decision making for autonomous systems.