Comparative branching-time semantics for Markov chains

  • Authors:

  • Christel Baier;Joost-Pieter Katoen;Holger Hermanns;Verena Wolf

  • Affiliations:

  • University of Bonn, Römerstraíe 164, D-53117 Bonn, Germany;RWTH Aachen, Ahornstraíe 55, D-52074 Aachen, Germany and University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Saarland University, D-66123 Saarbrücken, Germany and University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;University of Mannheim, D-68131 Mannheim, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2005

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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 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.