Revisiting Weak Simulation for Substochastic Markov Chains

  • David N. Jansen
  • Lei Song
  • Lijun Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8054)


The spectrum of branching-time relations for probabilistic systems has been investigated thoroughly by Baier, Hermanns, Katoen and Wolf (2003, 2005), including weak simulation for systems involving substochastic distributions. Weak simulation was proven to be sound w.r.t. the liveness fragment of the logic PCTL\(_{\setminus \mathcal{X}}\), and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness. In this paper, we present a novel definition that is sound for live PCTL\(_{\setminus \mathcal{X}}\), and a variant that is both sound and complete.

A long version of this article containing full proofs is available from [11].


Markov Chain Atomic Proposition Liveness Property Countable Support Simulation Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • David N. Jansen
    • 1
  • Lei Song
    • 2
    • 5
  • Lijun Zhang
    • 3
    • 4
    • 5
  1. 1.Model-Based System DevelopmentRadboud UniversiteitNijmegenThe Netherlands
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesBeijingChina
  4. 4.DTU ComputeTechnical University of DenmarkDenmark
  5. 5.Universität des SaarlandesSaarbrückenGermany

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