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FlyFast: A Scalable Approach to Probabilistic Model-Checking Based on Mean-Field Approximation

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10500))

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Abstract

Model-checking is an effective formal verification technique that has also been extended to quantitative logics and models such as PCTL and DTMCs as well as CSL and CTMCs/CTMDPs. Unfortunately, the state-space explosion problem of classical model-checking algorithms affects also quantitative extensions. Mean-field techniques provide approximations of the mean behaviour of large population models. These approximations are deterministic: a unique value of the fractions of agents in each state is computed for each time instant. A drastic reduction of the size of the model is obtained enabling the definition of an efficient model-checking algorithm. This paper is a survey of work we have done in the last few years in the area of mean-field approximated probabilistic model-checking. We start with a brief description of FlyFast, an on-the-fly model checker we have developed for approximated bounded PCTL model-checking, based on mean-field population DTMC approximation. Then we show an example of use of FlyFast in the context of Collective Adaptive Systems. We also discuss two additional interesting front-ends for FlyFast; the first one is a translation from CTMC-based population models and (a fragment of) CSL that allows for approximate probabilistic model-checking in the continuous stochastic time setting; the second one is a translation from a predicate-based process interaction language that allows for probabilistic model-checking of models based on components equipped both with behaviour and with attributes, on which predicates are defined that can be used in component interaction primitives.

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Notes

  1. 1.

    See, e.g. www.focas.eu/adaptive-collective-systems.

  2. 2.

    The technique can be applied also to a finite selection of individuals; in addition, systems with several distinct types of individuals can be dealt with. For the sake of simplicity, in the present paper we consider systems with many instances of a single individual only and we focus in the model-checking a single individual in such a context.

  3. 3.

    Tenth Workshop on Quantitative Aspects of Programming Languages, March 31 - April 1, 2012, Tallinn, Estonia.

  4. 4.

    http://www.quanticol.eu.

  5. 5.

    FlyFast (https://quanticol.github.io/jSAM/flyfast.html) is provided within the jSAM (java StochAstic Model Checker) framework which is an open source Eclipse plugin (https://quanticol.github.io/jSAM/).

  6. 6.

    In FlyFast, the notation \(\texttt {C[n]}\) is used for indicating n copies of state \({\texttt {C}}\).

  7. 7.

    It is worth stressing here that in the model of process interaction presented in [46], which FlyFast is based on, processes do not synchronize on actions explicitly (i.e. there is no notion of randez-vous here). Process interaction is only indirect, by means of the impact of the o.m.v. on individual transition probabilities.

  8. 8.

    We used a 1.86 GHz Intel Core 2 Duo with 4 GB. State space generation time of PRISM is not counted. The experiments are available in the FlyFast web site, showing that the latter has comparable performance. Worst-case complexity of both algorithms are also comparable.

  9. 9.

    We refer to [38, 42] for the characterisation of safe formulas and a related discussion.

  10. 10.

    We refer to [7, 8] for the definition of formula robustness.

  11. 11.

    See Theorem 5 of [7].

  12. 12.

    Stiff models are those whose rates differ several orders of magnitude.

  13. 13.

    More specifically, we use only the discretisation phase of uniformisation, and not the transient analysis part, that would require a further composition with a Poisson process.

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Acknowledgments

In the late 80’s of the previous century, Diego met Ed, who was chairing a Work Package of the EU Lotosphere project, in which Diego participated as well. At that time, Diego was fascinated by the early work on probabilistic process algebras by Scott Smolka, Kim Larsen and others and he was applying similar ideas to LOTOS, together with Paola Quaglia. At the same time, he was loving the work of Rom, supervised by Ed, on Bundle Event Structures as a mathematical model underlying a truly concurrent semantics for LOTOS. The obvious step was to start thinking of probabilistic extensions of Bundle Event Structures. Accidentally, Diego and Mieke had met at a Lotosphere workshop in The Hague and they found themselves nicely synchronised in their professional interests, and beyond ...

Not surprisingly, Diego moved to Twente where he spent 12 months, from july 1992 to june 1993, and together with Ed, Rom and Joost-Pieter, started investigating probabilistic, deterministically timed and stochastically timed Bundle Event Structures. This was the start of a lively friendship of the four of them as well as of a series of headaches when trying to find finite graph-like representations of such structures suitable for analysis. They have been struggling together for years, searching for cut-off events in those slippery structures. Eventually, Mieke moved to Italy and joined the group of cut-off events hunters. It was fun! Maybe we did not manage to completely master the analysis of quantitative Bundle Event Structures, but we are aware of a couple of things: our current work on probabilistic systems is rooted back to those days (and headaches ...) and our friendship too. All this thanks to Ed, who accepted having Diego around in Twente in 1992–93.

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Authors and Affiliations

  1. CNR-ISTI, Pisa, Italy

    Diego Latella & Mieke Massink

  2. Università di Firenze, Firenze, Italy

    Michele Loreti

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  1. Diego Latella
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Correspondence to Michele Loreti .

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Editors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Joost-Pieter Katoen

  2. University of Twente, Enschede, The Netherlands

    Rom Langerak

  3. University of Twente, Enschede, The Netherlands

    Arend Rensink

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Latella, D., Loreti, M., Massink, M. (2017). FlyFast: A Scalable Approach to Probabilistic Model-Checking Based on Mean-Field Approximation. In: Katoen, JP., Langerak, R., Rensink, A. (eds) ModelEd, TestEd, TrustEd. Lecture Notes in Computer Science(), vol 10500. Springer, Cham. https://doi.org/10.1007/978-3-319-68270-9_13

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