@article{
 title = {Comparative branching-time semantics for Markov chains},
 type = {article},
 year = {2005},
 pages = {149-214},
 volume = {200},
 websites = {http://www.sciencedirect.com/science/article/pii/S0890540105000441},
 publisher = {Elsevier},
 id = {b52099dd-a8ff-36b2-8677-2fa31b1bcb9d},
 created = {2016-02-15T08:58:38.000Z},
 file_attached = {false},
 profile_id = {bbb99b2d-2278-3254-820f-2de6d915ce63},
 last_modified = {2017-03-22T13:51:34.979Z},
 read = {false},
 starred = {false},
 authored = {true},
 confirmed = {true},
 hidden = {false},
 citation_key = {BKHW05},
 source_type = {article},
 private_publication = {false},
 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.},
 bibtype = {article},
 author = {Baier, C and Katoen, J.-P. and Hermanns, H and Wolf, V},
 journal = {Information and Computation}
}

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