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Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation

  • Chapter
Formal Methods for Dynamical Systems (SFM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7938))

Abstract

In this chapter, we will describe, in a tutorial style, recent work on the use of fluid approximation techniques in the context of stochastic model checking. We will discuss the theoretical background and the algorithms working out an example.

This approach is designed for population models, in which a (large) number of individual agents interact, which give rise to continuous time Markov chain (CTMC) models with a very large state space. We then focus on properties of individual agents in the system, specified by Continuous Stochastic Logic (CSL) formulae, and use fluid approximation techniques (specifically, the so called fast simulation) to check those properties. We will show that verification of such CSL formulae reduces to the computation of reachability probabilities in a special kind of time-inhomogeneous CTMC with a small state space, in which both the rates and the structure of the CTMC can change (discontinuously) with time. In this tutorial, we will discuss only briefly the theoretical issues behind the approach, like the decidability of the method and the consistency of the approximation scheme.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Geosciences, CNR/ISTI, University of Trieste, Pisa, Italy

    Luca Bortolussi

  2. Laboratory for the Foundations of Computer Science, School of Informatics, University of Edinburgh, UK

    Jane Hillston

Authors
  1. Luca Bortolussi
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  2. Jane Hillston
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Editor information

Editors and Affiliations

  1. Dipartimento di Scienze di Base e Fondamenti, Università di Urbino "Carlo Bo", , ,, Piazza della Repubblica 13, 61029, Urbino, Italy

    Marco Bernardo

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Den Dolech 2, 5612 AZ, Eindhoven, The Netherlands

    Erik de Vink

  3. Dipartimento di Informatica,, Università di Verona, Ca’ Vignal 2, Strada le Grazie 15, 37134, Verona, Italy

    Alessandra Di Pierro

  4. Department of Computing, Imperial College London, Huxley Building,180 Queen’s Gate, SW7 2BZ, London, UK

    Herbert Wiklicky

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Bortolussi, L., Hillston, J. (2013). Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation. In: Bernardo, M., de Vink, E., Di Pierro, A., Wiklicky, H. (eds) Formal Methods for Dynamical Systems. SFM 2013. Lecture Notes in Computer Science, vol 7938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38874-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-38874-3_4

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  • Print ISBN: 978-3-642-38873-6

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