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Comparative Branching-Time Semantics for Markov Chains

  • Christel Baier
  • Holger Hermanns
  • Joost-Pieter Katoen
  • Verena Wolf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2761)

Abstract

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 characterised in terms of the temporal logics PCTL and CSL. Apart from presenting various existing branching-time relations in a uniform manner, our contributions are: (i) weak simulation for DTMCs is defined, (ii) weak bisimulation equivalence is shown to coincide with weak simulation equivalence, (iii) logical characterisation of weak (bi)simulations are provided, and (iv) a classification of branching-time relations is presented, elucidating the semantics of DTMCs, CTMCs and their interrelation.

Keywords

Markov Chain Exit Rate Reachability Condition Atomic Proposition 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 2003

Authors and Affiliations

  • Christel Baier
    • 1
  • Holger Hermanns
    • 2
    • 3
  • Joost-Pieter Katoen
    • 2
  • Verena Wolf
    • 1
  1. 1.Institut für Informatik IUniversity of BonnBonnGermany
  2. 2.Department of Computer ScienceUniversity of TwenteEnschedeThe Netherlands
  3. 3.Department of Computer ScienceSaarland UniversitySaarbrückenGermany

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