Abstract
This paper focuses on optimizing probabilities of events of interest defined over general controlled discrete-time Markov processes. It is shown that the optimization over a wide class of ω-regular properties can be reduced to the solution of one of two fundamental problems: reachability and repeated reachability. We provide a comprehensive study of the former problem and an initial characterization of the (much more involved) latter problem. A case study elucidates concepts and techniques.
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