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Fast Verified SCCs for Probabilistic Model Checking

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Automated Technology for Verification and Analysis (ATVA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14215))

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Abstract

High-performance probabilistic model checkers like the Modest Toolset’s mcsta follow the topological ordering of an MDP’s strongly connected components (SCCs) to speed up the numerical analysis. They use hand-coded and -optimised implementations of SCC-finding algorithms. Verified SCC-finding implementations so far were orders of magnitudes slower than their unverified counterparts. In this paper, we show how to use a refinement approach with the Isabelle theorem prover to formally verify an imperative SCC-finding implementation that can be swapped in for mcsta ’s current unverified one. It uses the same state space representation as mcsta, avoiding costly conversions of the representation. We evaluate the verified implementation’s performance using an extensive benchmark, and show that its use does not significantly influence mcsta ’s overall performance. Our work exemplifies a practical approach to incrementally increase the trustworthiness of existing model checking software by replacing unverified components with verified versions of comparable performance.

Authors are listed in alphabetical order. This work was funded by NWO grant OCENW.KLEIN.311, the EU’s Horizon 2020 research and innovation programme under MSCA grant no. 101008233 (MISSION), and NWO VENI grant 639.021.754.

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Data Availability Statement

Our supplementary material, proofs, and the tools used to obtain the results presented in this paper are archived and available at DOI 10.4121/aff9f553-0e9e-4ec2-90e0-20c5b6152862 [21].

Notes

  1. 1.

    Note that the order of the refinement relations () is different from the assertions ().

  2. 2.

    Despite the error, we did not exclude this instance from the figures because the error is after the SCC computation, so mobench did not flag it as a problem—and ultimately, this provides an interesting insight.

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  1. University of Twente, Enschede, The Netherlands

    Arnd Hartmanns, Bram Kohlen & Peter Lammich

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  1. Arnd Hartmanns
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  2. Bram Kohlen
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Correspondence to Bram Kohlen .

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  1. Université Sorbonne Paris Nord, Villetaneuse, France

    Étienne André

  2. Singapore Management University, Singapore, Singapore

    Jun Sun

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Hartmanns, A., Kohlen, B., Lammich, P. (2023). Fast Verified SCCs for Probabilistic Model Checking. In: André, É., Sun, J. (eds) Automated Technology for Verification and Analysis. ATVA 2023. Lecture Notes in Computer Science, vol 14215. Springer, Cham. https://doi.org/10.1007/978-3-031-45329-8_9

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