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Weighted Lumpability on Markov Chains

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Book cover Perspectives of Systems Informatics (PSI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7162))

Abstract

This paper reconsiders Bernardo’s T-lumpability on continuous-time Markov chains (CTMCs). This notion allows for a more aggressive state-level aggregation than ordinary lumpability. We provide a novel structural definition of (what we refer to as) weighted lumpability, prove some elementary properties, and investigate its compatibility with linear real-time objectives. The main result is that the probability of satisfying a deterministic timed automaton specification coincides for a CTMC and its weigthed lumped analogue. The same holds for metric temporal logic formulas.

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Author information

Authors and Affiliations

  1. Software Modeling and Verification Group, RWTH Aachen University, Germany

    Arpit Sharma & Joost-Pieter Katoen

Authors
  1. Arpit Sharma
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  2. Joost-Pieter Katoen
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Editor information

Editors and Affiliations

  1. Computer Science Department, Carnegie Mellon University, 5000 Forbes Avenue, 15213-3891, Pittsburgh, PA, USA

    Edmund Clarke

  2. A.P. Ershov Institute of Informatics Systems Siberian Branch of the Russian Academy of Sciences, 6, Acad. Lavrentiev ave, Novosibirsk, 630090, Russia

    Irina Virbitskaite

  3. The University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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Sharma, A., Katoen, JP. (2012). Weighted Lumpability on Markov Chains. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds) Perspectives of Systems Informatics. PSI 2011. Lecture Notes in Computer Science, vol 7162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29709-0_28

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  • DOI: https://doi.org/10.1007/978-3-642-29709-0_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29708-3

  • Online ISBN: 978-3-642-29709-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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