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A finite Markov Decision Process (MDP) requires specification of a state space , an action (or control) space , and decision time points t. If all states are accessible from any other state, the action space will often equal the state space. While states, actions, and decisions characterize the observed changes in the process over time, the process moves from state i to state j with transition probability p(j | i, a), which we can also denote as ! pij .