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International Symposium on Trustworthy Global Computing

TGC 2013: Trustworthy Global Computing pp 297–314Cite as

On-the-fly Fast Mean-Field Model-Checking

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8358))

Abstract

A novel, scalable, on-the-fly model-checking procedure is presented to verify bounded PCTL properties of selected individuals in the context of very large systems of independent interacting objects. The proposed procedure combines on-the-fly model checking techniques with deterministic mean-field approximation in discrete time. The asymptotic correctness of the procedure is shown and some results of the application of a prototype implementation of the FlyFast model-checker are presented.

This research has been partially funded by the EU projects ASCENS (nr. 257414) and QUANTICOL (nr. 600708), and the IT MIUR project CINA.

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Notes

  1. 1.

    The term ‘mean field’ has its origin in statistical physics and is sometimes used with slightly different meaning in the literature. Here we intend the meaning as defined in [26].

  2. 2.

    Note that the transition probabilities of these selected objects at time t may depend on the occupancy measure of the system at t and therefore also the truth-values of the formulas may vary with time.

  3. 3.

    For notational simplicity we call the fragment PCTL as well.

  4. 4.

    In [26] object is used instead of process. We consider the two terms synonyms here.

  5. 5.

    For the purpose of the present paper, language expressivity is not a main concern.

  6. 6.

    Appropriate syntactical shorthands can be introduced for describing the initial state, e.g. \(\langle \mathtt{S[2000],E[100],I[200],R[0]} \rangle \) for 2000 objects initially in state S etc.

  7. 7.

    Of course, the choice of the first object is purely conventional. Furthermore, all the results which in the present paper are stated w.r.t. the first object of a system, are easily extended to finite subsets of objects in the system. For the sake of notation, in the rest of the paper, we stick to the first object convention.

  8. 8.

    The specific features of the sublanguage are not relevant for the purposes of the present paper and we leave their treatment out for the sake of simplicity.

  9. 9.

    Strictly speaking, the relevant components of the algorithm are instantiated to representations of the terms, sets and functions mentioned in this section. For the sake of notational simplicity, we often use the same notation both for mathematical objects and for their representations.

  10. 10.

    We use a \(1.86 GHz\) Intel Core 2 Duo with 4 GB. State space generation time of PRISM is not counted. The experiments are available at http://rap.dsi.unifi.it/~loreti/OFPMC/).

  11. 11.

    With a similar argument as for definition (4), noting that \({\mathbf M}^{(N)}({\mathbf C}) = {\mathbf M}^{(N)}({\mathbf C}'')\) and \({\mathbf C}_{[1]} = {\mathbf C}''_{[1]}\), it can be easily seen that also definition (5) is a good definition.

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Authors and Affiliations

  1. Istituto di Scienza e Tecnologie dell’Informazione ‘A. Faedo’, CNR, Pisa, Italy

    Diego Latella & Mieke Massink

  2. Università di Firenze, Firenze, Italy

    Michele Loreti

Authors
  1. Diego Latella
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  2. Michele Loreti
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  3. Mieke Massink
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Correspondence to Diego Latella .

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Editors and Affiliations

  1. Microsoft Research, Mountain View, California, USA

    Martín Abadi

  2. IMT Institute for Advanced Studies, Lucca, Italy

    Alberto Lluch Lafuente

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Latella, D., Loreti, M., Massink, M. (2014). On-the-fly Fast Mean-Field Model-Checking. In: Abadi, M., Lluch Lafuente, A. (eds) Trustworthy Global Computing. TGC 2013. Lecture Notes in Computer Science(), vol 8358. Springer, Cham. https://doi.org/10.1007/978-3-319-05119-2_17

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  • DOI: https://doi.org/10.1007/978-3-319-05119-2_17

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