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Probabilistic reachability for parametric Markov models

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Abstract

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 Θ(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 non-determinism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.

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Authors and Affiliations

  1. Saarland University, Saarbrücken, Germany

    Ernst Moritz Hahn & Holger Hermanns

  2. INRIA Grenoble, Rhône-Alpes, France

    Holger Hermanns

  3. DTU Informatics, Technical University of Denmark, Copenhagen, Denmark

    Lijun Zhang

Authors
  1. Ernst Moritz Hahn
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  2. Holger Hermanns
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  3. Lijun Zhang
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Correspondence to Ernst Moritz Hahn.

Additional information

Part of this work was done while L. Zhang was at Saarland University and Oxford University.

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Hahn, E.M., Hermanns, H. & Zhang, L. Probabilistic reachability for parametric Markov models. Int J Softw Tools Technol Transfer 13, 3–19 (2011). https://doi.org/10.1007/s10009-010-0146-x

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