The Power of Weighted Regularity-Preserving Multi Bottom-Up Tree Transducers

The expressive power of regularity-preserving ε-free weighted linear multi bottom-up tree transducers is investigated. These models have very attractive theoretical and algorithmic properties, but their expressive power is not well understood especially in the weighted setting. It is proved that despite the restriction to preserve regularity their power still exceeds that of composition chains of ε-free weighted linear extended top-down tree transducers with regular look-ahead, which are a natural super-class of weighted synchronous tree substitution grammars that are commonly used in statistical machine translation. In particular, the linguistically motivated discontinuous transformation of topicalization can be modeled by such multi bottom-up tree transducers, whereas composition chains of such extended top-down tree transducers cannot implement it. On the negative side, the inverse of topicalization cannot even be implemented by any such multi bottom-up tree transducers, which confirms their bottom-up nature. An interesting, promising, and widely applicable proof technique is used to prove those statements.