Sylvia Friese, Helmut Seidl and Sebastian Maneth. Earliest Normal Form and Minimization for Bottom-Up Tree Transducers. International Journal of Foundations of Computer Science, 22(7):1607-1623, 2011.
We show that for every deterministic bottom-up tree transducer, a unique equivalent transducer can be constructed which is minimal. The construction is based on a sequence of normalizing transformations which, among others, guarantee that non-trivial output is produced as early as possible. For a deterministic bottom-up transducer where every state produces either none or infinitely many outputs, the minimal transducer can be constructed in polynomial time.