Compositions of n tree transducers
William F. Ogden, William C. Rounds · 1972
Top-down tree transductions, introduced as models of syntax-directed translations and transformational grammars in [12] and [11], are not closed under relational composition. However, closure under relational composition is not always needed; for example, in establishing closure properties of surface sets.(Surface sets are tree-languages obtained as ranges of transductions.) One such closure property, whether the image of a surface set under a transduction is a surface set, remained open.