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This paper presents algorithms for identifying and reducing a dedicated setof controllable transition rates of a state-labelled continuous-time Markovchain model. The purpose of the reduction is to make states to satisfy a givenrequirement, specified as a CSL upper time-bounded Until formula. Wedistinguish two different cases, depending on the type of probability bound. Anatural partitioning of the state space allows us to develop possiblesolutions, leading to simple algorithms for both cases.

Rate Reduction for State-labelled Markov Chains with Upper Time-bounded CSL Requirements