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Kronecker Based Matrix Representations for Large Markov Models

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Validation of Stochastic Systems

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2925))

Abstract

State-based analysis of discrete event systems notoriously suffers from the largeness of state spaces, which often grow exponentially with the size of the model. Since non-trivial models tend to be built by submodels in some hierarchical or compositional manner, one way to achieve a compact representation of the associated state-transition system is to use Kronecker representations that accommodate the structure of a model at the level of a state transition system. In this paper, we present the fundamental idea of Kronecker representation and discuss two different kinds of representations, namely modular representations and hierarchical representations. Additionally, we briefly outline how the different representations can be exploited in efficient analysis algorithms.

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Author information

Authors and Affiliations

  1. Technische Universität Dresden, D-01062, Dresden, Germany

    Peter Buchholz

  2. Universität Dortmund, D-44221, Dortmund, Germany

    Peter Kemper

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  1. Peter Buchholz
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  2. Peter Kemper
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Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science, Technical University Dresden, Germany

    Christel Baier

  2. Centre for Telematics and Information Technology, Faculty for Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500, AE, Netherlands

    Boudewijn R. Haverkort

  3. VASY, INRIA, Grenoble Rhône-Alpes, France

    Holger Hermanns

  4. Software Modeling and Verification, RWTH Aachen University, Germany

    Joost-Pieter Katoen

  5. Institut für Technische Informatik, Universität der Bundeswehr München,  

    Markus Siegle

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Buchholz, P., Kemper, P. (2004). Kronecker Based Matrix Representations for Large Markov Models. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, JP., Siegle, M. (eds) Validation of Stochastic Systems. Lecture Notes in Computer Science, vol 2925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24611-4_8

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  • DOI: https://doi.org/10.1007/978-3-540-24611-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22265-1

  • Online ISBN: 978-3-540-24611-4

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