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[ABCK15] A. Abate, L. Brim, M. Ceska, M. Kwiatkowska. Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks. In Kroening, Daniel and Păsăreanu, Corina S. (editors), Proc. 27th International Conference on Computer Aided Verification (CAV), volume 9206 of LNCS, pages 195-213, Springer. 2015. [pdf] [bib]
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Notes: The original publication is available at link.springer.com.
Abstract. Quantitative analysis of Markov models typically proceeds through numerical methods or simulation-based evaluation. Since the state space of the models can often be large, exact or approximate state aggregation methods (such as lumping or bisimulation reduction) have been proposed to improve the scalability of the numerical schemes. However, none of the existing numerical techniques provides general, explicit bounds on the approximation error, a problem particularly relevant when the level of accuracy affects the soundness of verification results. We propose a novel numerical approach that combines the strengths of aggregation techniques (state-space reduction) with those of simulation-based approaches (automatic updates that adapt to the process dynamics). The key advantage of our scheme is that it provides rigorous precision guarantees under different measures. The new approach, which can be used in conjunction withtime uniformisation techniques, is evaluated on two models of chemical reaction networks, a signalling pathway and a prokaryotic gene expression network: it demonstrates marked improvement in accuracy without performance degradation, particularly when compared to known state-space truncation techniques.