On the Balancedness of Tree-to-Word Transducers

A language over an alphabet [Formula: see text] of opening ([Formula: see text]) and closing ([Formula: see text]) brackets, is balanced if it is a subset of the Dyck language [Formula: see text] over [Formula: see text], and it is well-formed if all words are prefixes of words in [Formula: see text]. We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time. With this at a hand we decide for the class 2-TW of non-linear tree transducers with output alphabet [Formula: see text] whether or not the output language is balanced.

Compositions of Tree-to-Tree Statistical Machine Translation Models

The well-known synchronous context-free grammars (SCFGs) and synchronous tree-substitution grammars (STSGs), both of which are used as tree-to-tree translation models in statistical machine translation are investigated. Their composition hierarchies are established in both the unweighted as well as the weighted case. More precisely, it is shown that SCFGs are closed under composition in both cases and that there is a close connection between compositions of STSGs and compositions of certain tree transducers. With the help of the close ties, the composition closure of STSGs is identified in both cases as well. The results for the weighted case utilize a new lifting technique that might prove useful also in similar setups.