Before revision:  Motivated by engineering considerations, we then consider a natural decomposition of any master equation that implements a given function into a sequence of "hidden" timesteps, demarcated by changes in the set of allowed transitions between states. We demonstrate a fundamental tradeoff between the number of hidden states and the number of hidden timesteps needed to implement any given f using master equation dynamics.
After revision:  Motivated by engineering considerations, we then consider a natural decomposition of any master equation that implements a given function into a sequence of "hidden" timesteps, demarcated by changes in what transitions are allowed under the rate matrix. Often there is a real-world cost for each additional hidden state, and for each additional hidden timestep. We derive the associated "space/time" tradeoff between the number of hidden states and the number of hidden timesteps needed to implement any given f using master equation dynamics.