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Probabilistic Reachability for Parametric Markov Models

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 5578)

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(logn)). 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.

This work is supported by the NWO-DFG bilateral project VOSS, by the DFG as part of the Transregional Collaborative Research Center SFB/TR 14 AVACS and the Graduiertenkolleg “Leistungsgarantien für Rechnersysteme”, and has received funding from the European Community’s Seventh Framework Programme under grant agreement no 214755.

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Hahn, E.M., Hermanns, H., Zhang, L. (2009). Probabilistic Reachability for Parametric Markov Models. In: Păsăreanu, C.S. (eds) Model Checking Software. SPIN 2009. Lecture Notes in Computer Science, vol 5578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02652-2_10

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  • DOI: https://doi.org/10.1007/978-3-642-02652-2_10

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