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 (Probabilistic Computation Tree Logic) and CSL (Continuous Stochastic Logic). 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.
|Publisher||University of Twente, Centre for Telematics and Information Technology (CTIT)|