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Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks

  • Alessandro Abate
  • Luboš Brim
  • Milan Češka
  • Marta Kwiatkowska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9206)

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 with time 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.

Keywords

Error Bound Chemical Master Equation Empirical Error Probabilistic Model Check Uniformisation Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alessandro Abate
    • 1
  • Luboš Brim
    • 2
  • Milan Češka
    • 1
    • 2
  • Marta Kwiatkowska
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK
  2. 2.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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