Probabilistic Reachability for Parametric Markov Models

Ernst Moritz Hahn, Holger Hermanns, Lijun Zhang

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    Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form function representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in the growth of the regular expression relative to the number of states (n(log n)).We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids this blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with nondeterminism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.
    Original languageEnglish
    JournalInternational Journal on Software Tools for Technology Transfer
    Issue number1
    Pages (from-to)3-19
    Publication statusPublished - 2011

    Bibliographical note

    The original publication is available at


    • Reachability
    • Model checking
    • Markov chains
    • Parametric model analysis


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