Weighted Lumpability on Markov Chains

  • Arpit Sharma
  • Joost-Pieter Katoen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7162)


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.


continuous-time Markov chain bisimulation weighted lumpability deterministic timed automaton metric temporal logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Arpit Sharma
    • 1
  • Joost-Pieter Katoen
    • 1
  1. 1.Software Modeling and Verification GroupRWTH Aachen UniversityGermany

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