[DHK13] Frits Dannenberg, Ernst Moritz Hahn and Marta Kwiatkowska. Computing Cumulative Rewards using Fast Adaptive Uniformisation. In Proc. 11th International Conference on Computational Methods in Systems Biology (CMSB'13), volume 8130 of LNCS, pages 33-49, Springer. September 2013. [pdf] [bib] [Develops fast adaptive uniformisation techniques for cumulative reward properties, implemented in PRISM.]
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Notes: PRISM files for the DNA walker examples used in the paper can be found here. The original publication is available at link.springer.com.
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Abstract. The computation of transient probabilities for continuous-time Markov chains often employs uniformisation, also known as the Jensen’s method. The fast adaptive uniformisation method introduced by Mateescu approximates the probability by neglecting insignificant states, and has proven to be effective for quantitative analysis of stochastic models arising in chemical and biological applications. However, this method has only been formulated for the analysis of properties at a given point of time t. In this paper, we extend fast adaptive uniformisation to handle expected reward properties which reason about the model behaviour until time t, for example, the expected number of chemical reactions that have occurred until t. To show the feasibility of the approach, we integrate the method into the probabilistic model checker PRISM and apply it to a range of biological models, demonstrating superior performance compared to existing techniques.