A bottom-up characterization of deterministic top-down tree transducers with regular look-ahead

In the theory of tree automata and tree transducers mai nly two different ways to process trees are conside One is the bottom-up processing, which starts at the leaves of a tree s and ends up in the root of s. The other one is the top-down processing, when the process starts at the root of s and proceeds towards the leaves of . Therefore the literature distinguishes between bottom-up (or: frontier-to-root) and top-down (o r: root-to-frontier) tree automata tree transducers, and tree-to-graph transducers [17–19,5,6,1,15,16,12]. The different ways of processing may deliver different results, e.g., the recognizing capacity of determ top-down tree automata is less than that of deterministic bottom-up tree automata [15,16], the classes of b and of top-down tree transformations are incomparable with respect to inclusion [5], and the class of lin down tree transformations is a proper subclass of the class of linear bottom-up tree transformations [5]. On hand, (nondeterministic) bottom-up and top-down tree automata recognize the same class of tree language linear and nondeleting bottom-up and top-down tree transducers compute the same class of tree transfo [5], and tree-generating bottom-up and top-down tree-to-graph transducers are equivalent [12]. In [6] a bottom-up capability, namely inspecting subtrees before performing a computation step, was a top-down tree transducers in order to have nicer closure properties than the top-down tree transducers h capability is called regular look-ahead, and the tree transdu cers obtained are called top-down tree transducers regular look-ahead. By adding this botto m-up capability to top-down tree trans ducers, they get closer to bottom