Approximate planning and verification for large markov decision processes

We study the planning and verification problems for very large or infinite probabilistic systems, like Markov Decision Processes (MDPs), from a complexity point of view. More precisely, we deal with the problem of designing an efficient approximation method to compute a near-optimal policy for the planning problem of MDPs and the satisfaction probabilities of interesting properties like reachability or safety, over the Markov chain obtained by restricting the MDP to the near-optimal policy. The complexity of the approximation method is independent of the size of the state space and uses only a probabilistic generator of the MDP.