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The How and Why of Interactive Markov Chains

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Formal Methods for Components and Objects (FMCO 2009)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6286))

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Abstract

This paper reviews the model of interactive Markov chains (IMCs, for short), an extension of labelled transition systems with exponentially delayed transitions. We show that IMCs are closed under parallel composition and hiding, and show how IMCs can be compositionally aggregated prior to analysis by e.g., bisimulation minimisation or aggressive abstraction based on simulation pre-congruences. We survey some recent analysis techniques for IMCs, i.e., explaining how measures such as reachability probabilities can be obtained. Finally, we demonstrate that IMCs are a natural (and simple) semantic model for stochastic process algebras and generalised stochastic Petri nets and can be used for engineering formalisms such as AADL and dynamic fault trees.

This research has been funded by NWO under grant 612.000.420 (QUPES) and DFG-NWO grant Dn 63-257 (ROCKS), by the EU under FP7-ICT-2007-1 grant 214755 (Quasimodo), and by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” SFB/TR 14 AVACS.

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Authors and Affiliations

  1. Dependable Systems and Software, Universität des Saarlandes, Germany

    Holger Hermanns

  2. VASY Team, INRIA Grenoble – Rhône-Alpes, France

    Holger Hermanns

  3. MOVES Group, RWTH Aachen University, Germany

    Joost-Pieter Katoen

  4. FMT Group, University of Twente, The Netherlands

    Joost-Pieter Katoen

Authors
  1. Holger Hermanns
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  2. Joost-Pieter Katoen
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Editors and Affiliations

  1. Centre for Mathematics and Computer Science, CWI, Science Park 123, 1098, Amsterdam, XG, The Netherlands

    Frank S. de Boer

  2. Leiden Institute of Advanced Computer Science, Leiden University, P.O. Box 9512, 2300, Leiden, RA, The Netherlands

    Marcello M. Bonsangue

  3. Heinrich-Heine University of Dusseldorf, Dusseldorf, Germany

    Stefan Hallerstede

  4. Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany

    Michael Leuschel

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Hermanns, H., Katoen, JP. (2010). The How and Why of Interactive Markov Chains. In: de Boer, F.S., Bonsangue, M.M., Hallerstede, S., Leuschel, M. (eds) Formal Methods for Components and Objects. FMCO 2009. Lecture Notes in Computer Science, vol 6286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17071-3_16

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  • DOI: https://doi.org/10.1007/978-3-642-17071-3_16

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