Abstract
Compositions of well-known tree-to-tree translation models used in statistical machine translation are investigated. Synchronous context-free grammars are closed under composition in both the unweighted as well as the weighted case. In addition, it is demonstrated that there is a close connection between compositions of synchronous tree-substitution grammars and compositions of certain tree transducers because the intermediate trees can encode finite-state information. Utilizing these close ties, the composition closure of synchronous tree-substitution grammars is identified in the unweighted and weighted case. In particular, in the weighted case, these results build on a novel lifting strategy that will prove useful also in other setups.
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