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International Conference on Formal Modeling and Analysis of Timed Systems

FORMATS 2017: Formal Modeling and Analysis of Timed Systems pp 153–169Cite as

Symbolic Dependency Graphs for \(\text {PCTL}^{>}_{\le }\) Model-Checking

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10419))

Abstract

We consider the problem of model-checking a subset of probabilistic CTL, interpreted over (discrete-time) Markov reward models, allowing the specification of lower bounds on the probability of the set of paths satisfying a cost-bounded path formula. We first consider a reduction to fixed-point computations on a graph structure that encodes a division of the problem into smaller sub-problems by explicit unfolding of the given formula into sub-formulae. Although correct, the size of the graph constructed is highly dependent on the size of the cost bound. To this end, we provide a symbolic extension, effectively ensuring independence between the size of the graph and the cost-bound.

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Notes

  1. 1.

    Note that using costs from \(\mathbb {Q}^+\) does not change the expressivity of the formalism; as any model is finite, one can always multiply all costs by the least common denominator to obtain a model with costs in \(\mathbb {N}^+\).

  2. 2.

    Any such transition could be replaced by a number of unit length transitions with probability 1, transforming the MRM into a (much larger) Markov chain.

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Authors and Affiliations

  1. Department of Computer Science, Aalborg University, Selma Lagerlöfs Vej 300, 9220, Aalborg, Denmark

    Anders Mariegaard & Kim Guldstrand Larsen

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  1. Anders Mariegaard
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  2. Kim Guldstrand Larsen
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Correspondence to Anders Mariegaard .

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Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, United Kingdom

    Alessandro Abate

  2. Dept. d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Gilles Geeraerts

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Mariegaard, A., Larsen, K.G. (2017). Symbolic Dependency Graphs for \(\text {PCTL}^{>}_{\le }\) Model-Checking. In: Abate, A., Geeraerts, G. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2017. Lecture Notes in Computer Science(), vol 10419. Springer, Cham. https://doi.org/10.1007/978-3-319-65765-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-65765-3_9

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