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Markov decision processes (MDPs) are often used for modelling distributed systems with probabilistic failure or randomisation. We consider the problem of model repair for MDPs defined as follows: if the MDP fails to satisfy a property, we aim to find new values for the transition probabilities so that the property is guaranteed to hold, while at the same time the cost of repair is minimised. Because...
We propose a novel stochastic extension of timed automata, i.e. Markovian Timed Automata. We study the problem of optimizing time-bounded reachability probabilities in this model, i.e., the maximum likelihood to hit a set of goal locations within a given deadline. We propose Bellman equations to characterize the probability, and provide two approaches to solve the Bellman equations, namely, a discretization...
We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise...
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