The power of tree series transducers of type I and II is studied for IO as well as OI tree series substitution. More precisely, it is shown that the IO tree series transformations of type I (respectively, type II) are characterized by the composition of homomorphism top-down IO tree series transformations with bottom-up (respectively, linear bottom-up) IO tree series transformations. On the other hand, polynomial OI tree series transducers of type I and II and top-down OI tree series transducers are equally powerful.
['Andreas Maletti']
The power of tree series transducers of type i and II