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.

EARLIEST NORMAL FORM AND MINIMIZATION FOR BOTTOM-UP TREE TRANSDUCERS

We show that for every deterministic bottom-up tree transducer, a unique equivalent transducer can be constructed which is minimal. The construction is based on a sequence of normalizing transformations which, among others, guarantee that non-trivial output is produced as early as possible. For a deterministic bottom-up transducer where every state produces either none or infinitely many outputs, the minimal transducer can be constructed in polynomial time.

An alternative to synchronous tree substitution grammars

Synchronous tree substitution grammars (stsg) are a (formal) tree transformation model that is used in the area of syntax-based machine translation. A competitor that is at least as expressive as stsg is proposed and compared to stsg. The competitor is the extended multi bottom-up tree transducer (mbot), which is the bottom-up analogue with the additional feature that states have non-unary ranks. Unweighted mbot have already been investigated with respect to their basic properties, but the particular properties of the constructions that are required in the machine translation task are largely unknown. stsg and mbot are compared with respect to binarization, regular restriction, and application. Particular attention is paid to the complexity of the constructions.

Training Tree Transducers

Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Tree-based modeling still lacks many of the standard tools taken for granted in (finite-state) string-based modeling. The theory of tree transducer automata provides a possible framework to draw on, as it has been worked out in an extensive literature. We motivate the use of tree transducers for natural language and address the training problem for probabilistic tree-to-tree and tree-to-string transducers.

DECIDABILITY OF THE SHAPE PRESERVING PROPERTY OF BOTTOM-UP TREE TRANSDUCERS

It is a known result that both shape preserving top-down tree transducers and shape preserving bottom-up tree transducers are semantically equivalent to finite state relabeling tree transducers. Moreover, it is also known that the shape preserving property of top-down tree transducers is decidable. In this paper we present an analogous result for bottom-up tree transducers: we show that it is also decidable whether a bottom-up tree transducer is shape preserving or not.