  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.
