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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Computing Conditional Probabilities in Markovian Models Efficiently
verfasst von : Christel Baier, Joachim Klein, Sascha Klüppelholz, Steffen Märcker
Erschienen in: Tools and Algorithms for the Construction and Analysis of Systems
Verlag: Springer Berlin Heidelberg
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The fundamentals of probabilistic model checking for Markovian models and temporal properties have been studied extensively in the past 20 years. Research on methods for computing conditional probabilities for temporal properties under temporal conditions is, however, comparably rare. For computing conditional probabilities or expected values under
ω
-regular conditions in Markov chains, we introduce a new transformation of Markov chains that incorporates the effect of the condition into the model. For Markov decision processes, we show that the task to compute maximal reachability probabilities under reachability conditions is solvable in polynomial time, while it was conjectured to be computationally hard. Using adaptions of known automata-based methods, our algorithm can be generalized for computing the maximal conditional probabilities for
ω
-regular events under
ω
-regular conditions. The feasibility of our algorithms is studied in two benchmark examples.