Comparative branching-time semantics for Markov chains

Christel BaierChristel Baier, Joost-Pieter KatoenJoost-Pieter Katoen, Holger HermannsHolger Hermanns, Verena WolfVerena Wolf

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Christel Baier, Joost-Pieter Katoen, Holger Hermanns, Verena Wolf
Comparative branching-time semantics for Markov chains
Information and Computation, 200(2):149--214, 2005

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KurzfassungAbstract
This paper presents various semantics in the branching-time spectrum of discrete-time and continuous-time Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation pre-orders are covered and are logically characterized in terms of the temporal logics Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic (CSL). Apart from presenting various existing branching-time relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and pre-orders in the continuous- and discrete-time setting. The results are summarized in a branching-time spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship.
Forschungsgruppe:Research Group: Algebraische und logische Grundlagen der InformatikAlgebraic and Logical Foundations of Computer Science

@article{BKHW2005,
  author  = {Christel Baier and Joost-Pieter Katoen and Holger Hermanns and
             Verena Wolf},
  title   = {Comparative branching-time semantics for Markov chains},
  journal = {Information and Computation},
  volume  = {200},
  number  = {2},
  year    = {2005},
  pages   = {149--214},
  doi     = {10.1016/J.IC.2005.03.001}
}