Quantitative model-checking of controlled discrete-time Markov processes
  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 $\omega$-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 characterisation of the (much more involved) latter problem. A case study elucidates concepts and techniques. 
Ilya Tkachev, Alexandru Mereacre, Joost-Pieter Katoen, Alessandro   Abate
math.PR cs.FL cs.SY math.OC