# Graph-Based Reductions for Model Checking and Learning MDPs

Omega-regular objectives in Markov decision processes (MDPs) reduce to reachability: find a policy which maximizes the probability of reaching a target set of states. Given an MDP, an initial distribution, and a target set of states, such a policy can be computed by most probabilistic model checking tools. If the MDP is only partially specified, i.e., some prob- abilities are unknown, then model-learning techniques can be used to statistically approximate the probabilities and enable the computation of the desired policy. For fully specified MDPs, reducing the size of the MDP translates into faster model checking; for partially specified MDPs, into faster learning. We provide reduction techniques that allow us to remove irrelevant transition probabilities: transition probabilities (known, or to be learned) that do not influence the maximal reachability probability. Among other applications, these reductions can be seen as a pre-processing of MDPs before model checking or as a way to reduce the number of experiments required to obtain a good approximation of an unknown MDP.