The existence of refinement mappings
Theoretical Computer Science
Three logics for branching bisimulation
Journal of the ACM (JACM)
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Approximating labelled Markov processes
Information and Computation
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Approximate Analysis of Probabilistic Processes: Logic, Simulation and Games
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Testing Finitary Probabilistic Processes
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Comparative branching-time semantics for Markov chains
Information and Computation
On Probabilistic Automata in Continuous Time
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
A general framework for probabilistic characterizing formulae
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
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The spectrum of branching-time relations for probabilistic systems has been investigated thoroughly by Baier, Hermanns, Katoen and Wolf (2003, 2005), including weak simulation for systems involving substochastic distributions. Weak simulation was proven to be sound w.r.t. the liveness fragment of the logic PCTL$_{\setminus \mathcal{X}}$, and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness. In this paper, we present a novel definition that is sound for live PCTL$_{\setminus \mathcal{X}}$, and a variant that is both sound and complete. A long version of this article containing full proofs is available from [11].