Before revision:  As we show , any function f over a set of "visible" states X can be implemented--if the master equation implementing f has access to some additional "hidden" states not in X. 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.
After revision:  As we show , any function f over a set of "visible" states X can be implemented--if the master equation implementing f has access to some additional "hidden" states are dynamically coupled to those visible states. We also show that 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.