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On-the-fly verification and optimization of DTA-properties for large Markov chains

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Abstract

We consider continuous-time Markov chains (CTMC) with very large or infinite state spaces which are, for instance, used to model biological processes or to evaluate the performance of computer and communication networks. We propose a numerical integration algorithm to approximate the probability that a process conforms to a specification that belongs to a subclass of deterministic timed automata (DTAs). We combat the state space explosion problem by using a dynamic state space that contains only the most relevant states. In this way we avoid an explicit construction of the state-transition graph of the composition of the DTA and the CTMC. We also show how to maximize the probability of acceptance of the DTA for parametric CTMCs and substantiate the usefulness of our approach with experimental results from biological case studies.

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Notes

  1. For simplicity, we choose a fixed step size here. In our implementation h is adaptive.

  2. Note that the chain rule is applicable, since Q as well as π(t) depend on λ.

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Acknowledgements

This research has been partially funded by the German Research Council (DFG) as part of the Cluster of Excellence on Multimodal Computing and Interaction at Saarland University and the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).

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Correspondence to Verena Wolf.

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Mikeev, L., Neuhäußer, M.R., Spieler, D. et al. On-the-fly verification and optimization of DTA-properties for large Markov chains. Form Methods Syst Des 43, 313–337 (2013). https://doi.org/10.1007/s10703-012-0165-1

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