Composition Closure of Linear Extended Top-down Tree Transducers

Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations. The expressive power of compositions of such transducers with and without regular look-ahead is investigated. In particular, the restrictions of nondeletion, epsilon-freeness, and strictness are considered. The composition hierarchy turns out to be finite for all epsilon-free (all rules consume input) variants of these transducers except for nondeleting epsilon-free linear extended top-down tree transducers. The least number of transducers needed for the full expressive power of arbitrary compositions is presented. In all remaining cases (including nondeleting epsilon-free linear extended top-down tree transducers) the composition hierarchy does not collapse.