This paper proposes a novel abstraction technique for continuous-time Markov chains (CTMCs). Our technique fits within the realm of three-valued abstraction methods that have been used successfully for traditional model checking. The key idea is to apply abstraction on uniform CTMCs that are readily obtained from general CTMCs, and to abstract transition probabilities by intervals. It is shown that this provides a conservative abstraction for both true and false for a threevalued semantics of the branching-time logic CSL (Continuous Stochastic Logic). Experiments on an infinite-state CTMC indicate the feasibility of our abstraction technique.

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Abstract. We propose to exploit three-valued abstraction to stochastic systems in a compositional way. This combines the strengths of an aggressive state-based abstraction technique with compositional modeling. Applying this principle to interactive Markov chains yields abstract models that combine interval Markov chains and modal transition systems in a natural and orthogonal way. We prove the correctness of our technique for parallel and symmetric composition and show that it yields lower bounds for minimal and upper bounds for maximal timed reachability probabilities.

This paper studies quantitative model checking of infinite tree-like (continuous-time) Markov chains. These treestructured quasi-birth death processes are equivalent to probabilistic pushdown automata and recursive Markov chains and are widely used in the field of performance evaluation. We determine time-bounded reachability probabilities in these processeswhich with direct methods, i.e., uniformization, results in an exponential blow-up-by applying abstraction. We contrast abstraction based on Markov decision processes (MDPs) and interval-based abstraction; study various schemes to partition the state space, and empirically show their influence on the accuracy of the obtained reachability probabilities. Results show that gridlike schemes, in contrast to chain-and tree-like ones, yield extremely precise approximations for rather coarse abstractions. D. Klink has been funded by the DFG Research Training Group 1298 (AlgoSyn) and the EU FP7 project QUASIMODO. A. Remke has been funded by the NWO project MC=MC (612.000.311) and by 3TU.CeDiCT.

Abstract. This paper proposes a novel abstraction technique based on Erlang's method of stages for continuous-time Markov chains (CTMCs). As abstract models Erlang-k interval processes are proposed where state residence times are governed by Poisson processes and transition probabilities are specified by intervals. We provide a three-valued semantics of CSL (Continuous Stochastic Logic) for Erlang-k interval processes, and show that both affirmative and negative verification results are preserved by our abstraction. The feasibility of our technique is demonstrated by a quantitative analysis of an enzyme-catalyzed substrate conversion, a well-known case study from biochemistry.