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Are Parametric Markov Chains Monotonic?

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Automated Technology for Verification and Analysis (ATVA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11781))

Abstract

This paper presents a simple algorithm to check whether reachability probabilities in parametric Markov chains are monotonic in (some of) the parameters. The idea is to construct—only using the graph structure of the Markov chain and local transition probabilities—a pre-order on the states. Our algorithm cheaply checks a sufficient condition for monotonicity. Experiments show that monotonicity in several benchmarks is automatically detected, and monotonicity can speed up parameter synthesis up to orders of magnitude faster than a symbolic baseline.

Supported by the DFG RTG 2236 “UnRAVeL”.

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Notes

  1. 1.

    The complement of the parameter feasibility problem.

  2. 2.

    That is, \(G = (S,E)\) with \(E = \{(s,t) \mid s,t \in S \wedge s \preceq _{}t \wedge (\not \exists s'\in S.~s\preceq _{}s' \preceq _{}t)\} \).

  3. 3.

    Although monotonicity is not explicitly mentioned in [40].

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Authors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Jip Spel, Sebastian Junges & Joost-Pieter Katoen

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  1. Jip Spel
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Correspondence to Jip Spel .

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  1. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Yu-Fang Chen

  2. DENSO AUTOMOTIVE Deutschland GmbH, Eching, Germany

    Chih-Hong Cheng

  3. Institute of Computer Science, TU München, Munich, Germany

    Javier Esparza

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Spel, J., Junges, S., Katoen, JP. (2019). Are Parametric Markov Chains Monotonic?. In: Chen, YF., Cheng, CH., Esparza, J. (eds) Automated Technology for Verification and Analysis. ATVA 2019. Lecture Notes in Computer Science(), vol 11781. Springer, Cham. https://doi.org/10.1007/978-3-030-31784-3_28

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  • DOI: https://doi.org/10.1007/978-3-030-31784-3_28

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