Tree Series Transformations that Respect Copying

Abstract

We consider tree series transducers which were introduced in [EFV], and define the tree-to-tree series transformations computed by them in two different ways. One of the definitions is based on the ←-substitution of tree series taken from [EFV] while the other one is based on a new tree series substitution introduced in this paper. This new substitution is called -substitution and the main difference between the ←- and the -substitutions is that the first one does not take into account the number of the occurrences of the substitution variables while the second one does. We compare the two different ways of computing tree-to-tree series transformations and show that, for the -substitution, fundamental relations from the theory of tree transducers carry over to tree series transducers.