Model checking and abstraction
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Journal of the ACM (JACM)
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AsiaMS '07 Proceedings of the IASTED Asian Conference on Modelling and Simulation
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CAV'07 Proceedings of the 19th international conference on Computer aided verification
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CAV'07 Proceedings of the 19th international conference on Computer aided verification
Three-valued abstractions of Markov chains: completeness for a sizeable fragment of PCTL
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
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EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
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ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
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FMCO'09 Proceedings of the 8th international conference on Formal methods for components and objects
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VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
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LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
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Information Processing Letters
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QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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Information and Computation
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Theoretical Computer Science
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Information and Computation
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In this paper the abstraction-refinement paradigm based on 3-valued logics is extended to the setting of probabilistic systems. We define a notion of abstraction for Markov chains. To be able to relate the behavior of abstract and concrete systems, we equip the notion of abstraction with the concept of simulation. Furthermore, we present model checking for abstract probabilistic systems (abstract Markov chains) with respect to specifications in probabilistic temporal logics, interpreted over a 3-valued domain. More specifically, we introduce a 3-valued version of probabilistic computation-tree logic (PCTL) and give a model checking algorithm w.r.t. abstract Markov chains.