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Computing Conditional Probabilities: Implementation and Evaluation

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Software Engineering and Formal Methods (SEFM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10469))

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Abstract

Conditional probabilities and expectations are an important concept in the quantitative analysis of stochastic systems, e.g., to analyze the impact and cost of error handling mechanisms in rare failure scenarios or for a utility-analysis assuming an exceptional shortage of resources. This paper reports on the main features of an implementation of computation schemes for conditional probabilities in discrete-time Markov chains and Markov decision processes within the probabilistic model checker Prism and a comparative experimental evaluation. Our implementation has full support for computing conditional probabilities where both the objective and condition are given as linear temporal logic formulas, as well as specialized algorithms for reachability and other simple types of path properties. In the case of Markov chains we provide implementations for three alternative methods (quotient, scale and reset). We support Prism’s explicit and (semi-)symbolic engines. Besides comparative studies exploring the three dimensions (methods, engines, general vs. special handling), we compare the performance of our implementation and the probabilistic model checker Storm that provides facilities for conditional probabilities of reachability properties.

The authors are supported by the DFG through the collaborative research centre HAEC (SFB 912) and the Excellence Initiative by the German Federal and State Governments (cluster of excellence cfaed) and projects BA 1679/11-1 and 1679/12-1.

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Notes

  1. 1.

    In the context of a conditional probability \(\mathrm {Pr}(\varphi | \psi )\) we refer to \(\varphi \) as the objective and to \(\psi \) as the condition.

  2. 2.

    Prism’s explicit engine uses sparse matrix representation for the system and carries out all computation in an explicit manner, while the other three engines use multi-terminal binary decision diagrams (MTBDDs) for the model construction. The mtbdd engine is purely MTBDD-based. The hybrid engine uses an MTBDD-representation for the system and an explicit probability vector [38], while the sparse engine uses sparse matrices for the numerical computations.

  3. 3.

    https://wwwtcs.inf.tu-dresden.de/ALGI/PUB/SEFM17.

  4. 4.

    2 \(\times \) Intel Xeon E5-2680 (Octa Core, Sandy Bridge) @ 2.70 GHz, 384 GB RAM; Turbo Boost and Hyper Threading enabled; Debian GNU/Linux 8.3.

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Authors and Affiliations

  1. Institute of Theoretical Computer Science, Technische Universität Dresden, 01062, Dresden, Germany

    Steffen Märcker, Christel Baier, Joachim Klein & Sascha Klüppelholz

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  1. Steffen Märcker
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  2. Christel Baier
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  3. Joachim Klein
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  4. Sascha Klüppelholz
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Correspondence to Steffen Märcker .

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Editors and Affiliations

  1. University of Trento, Trento, Italy

    Alessandro Cimatti

  2. Mälardalen University, Västerås, Sweden

    Marjan Sirjani

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Märcker, S., Baier, C., Klein, J., Klüppelholz, S. (2017). Computing Conditional Probabilities: Implementation and Evaluation. In: Cimatti, A., Sirjani, M. (eds) Software Engineering and Formal Methods. SEFM 2017. Lecture Notes in Computer Science(), vol 10469. Springer, Cham. https://doi.org/10.1007/978-3-319-66197-1_22

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