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International GI/ITG Conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance

MMB&DFT 2012: Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance pp 121–135Cite as

Weighted Probabilistic Equivalence Preserves ω-Regular Properties

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7201))

Abstract

Equivalence relations can be used to reduce the state space of a system model, thereby permitting more efficient analysis. This paper extends the notion of weighted lumpability (WL) defined on continuous-time Markov chains (CTMCs) to the discrete-time setting, i.e., discrete-time Markov chains (DTMCs). We provide a structural definition of weighted probabilistic equivalence (WPE), define the quotient under WPE and prove some elementary properties. We show that ω-regular properties are preserved when reducing the state space of a DTMC using WPE. Finally, we show that WPE is compositional w.r.t. synchronous parallel composition.

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Author information

Authors and Affiliations

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

    Arpit Sharma

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  1. Arpit Sharma
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Editor information

Editors and Affiliations

  1. disco - Distributed Computer Systems Lab, Computer Science Department, University of Kaiserslautern, Building 36, P.O. Box 3049, 67663, Kaiserslautern, Germany

    Jens B. Schmitt

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Sharma, A. (2012). Weighted Probabilistic Equivalence Preserves ω-Regular Properties. In: Schmitt, J.B. (eds) Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance. MMB&DFT 2012. Lecture Notes in Computer Science, vol 7201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28540-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-28540-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28539-4

  • Online ISBN: 978-3-642-28540-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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