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

The expressive power of regularity-preserving [Formula: see text]-free weighted linear multi bottom-up tree transducers is investigated. These models have very attractive theoretical and algorithmic properties, but (especially in the weighted setting) their expressive power is not well understood. Despite the regularity-preserving restriction, their power still exceeds that of composition chains of [Formula: see text]-free weighted linear extended top-down tree transducers with regular look-ahead. The latter devices are a natural super-class of weighted synchronous tree substitution grammars, which are commonly used in syntax-based statistical machine translation. In particular, the linguistically motivated discontinuous transformation of topicalization can be modeled by such multi bottom-up tree transducers, whereas the mentioned composition chains cannot implement it. On the negative side, the inverse of topicalization cannot be implemented by any such multi bottom-up tree transducer, which confirms their bottom-up nature (and non-closure under inverses). An interesting, promising, and widely applicable proof technique is used to prove these statements.