We are interested only in transducers without useless states, that is, those in which for every state in T , there is a path leading to a final state.
if we further assume that P T P (s, t) is zero when no translation form exists for (s, t) in T , it can be easily verified that P T P is a joint distribution on Σ × ∆ which will be called the stochastic translation defined by T P .