Extended Top-down Tree Transducers Research Articles

Compositions of Weighted Extended Tree Transducers — The Unambiguous Case

Generalizations of another two open conjectures, Conjectures 13 and 14, of [Lagoutte, Maletti: Survey — Weighted extended top-down tree transducers — Part III: Composition. Proc. AFCS, LNCS 7020, p. 272–308, Springer 2011] are verified. It is proved that the composition of an unambiguous weighted extended tree transducer [Formula: see text] with a nondeleting weighted top-down tree transducer [Formula: see text] can be computed by a single weighted extended tree transducer. Extending the recent confirmation of Conjecture 11 it is also proved that the composition succeeds for any weighted top-down tree transducer [Formula: see text] (even if it is not nondeleting) if the unambiguous weighted extended tree transducer [Formula: see text] is constant.

Compositions of Weighted Extended Top-Down Tree Transducers

Compositions of Weighted Extended Top-Down Tree Transducers

Compositions with Constant Weighted Extended Tree Transducers

Conjecture 11 of [Lagoutte, Maletti: Survey — Weighted extended top-down tree transducers — Part III: Composition. Proc. AFCS, LNCS 7020, p. 272–308, Springer 2011] is confirmed. It is demonstrated that the composition of a constant weighted extended tree transducer with a linear weighted top-down tree transducer can be computed by a single weighted extended tree transducer. Whereas linearity and the top-down property are syntactic, the constant property is semantic. The decidability of the constant property is investigated in several restricted settings.

Composition Closure of Linear Extended Top-down Tree Transducers

Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations that are extensively used in syntax-based statistical machine translation. The expressive power of compositions of such transducers with and without regular look-ahead is investigated. In particular, the restrictions of ź-freeness, strictness, and nondeletion are considered. The composition hierarchy turns out to be finite for all ź-free (all rules consume input) variants of these transducers except for the nondeleting ź-free transducers. The least number of transducers needed for the full expressive power of arbitrary compositions is presented. In all remaining cases (incl. the nondeleting ź-free transducers) the composition hierarchy does not collapse.

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.

Survey: Weighted Extended Top-down Tree Transducers Part II—Application in Machine Translation

In this second part of the survey, we present the application of weighted extended top-down tree transducers in machine translation, which is the automatic translation of natural language texts. We present several formal properties that are relevant to machine translation and evaluate the weighted extended top-down tree transducer along those criteria. In addition, we demonstrate how to extract rules for an extended top-down tree transducer from existing linguistic data and how to obtain suitable rule weights automatically from similar information. Overall, the aim of the survey is twofold. It should provide a synopsis that illustrates how theory (tree transducers) and practice (machine translation) interact on this particular example. Secondly, it presents a uniform and simplified treatment of the rule extraction and training algorithms that is accessible to the nonexpert. Additional details can be found in the original results that are referenced throughout the text.

Survey: Weighted Extended Top-down Tree Transducers Part I - Basics and Expressive Power

Weighted extended top-down tree transducers (transducteurs généralisés descendants [Arnold, Dauchet: Bi-transductions de forêts. ICALP'76. Edinburgh University Press, 1976]) received renewed interest in the field of Natural Language Processing, where they are used in syntax-based machine translation. This survey presents the foundations for a theoretical analysis of weighted extended top-down tree transducers. In particular, it discusses essentially complete semirings, which are a novel concept that can be used to lift incomparability results from the unweighted case to the weighted case even in the presence of infinite sums. In addition, several equivalent ways to define weighted extended top-down tree transducers are presented and the individual benefits of each presentation is shown on a small result.

Compositions of extended top-down tree transducers

Unfortunately, the class of transformations computed by linear extended top-down tree transducers with regular look-ahead is not closed under composition. It is shown that the class of transformations computed by certain linear bimorphisms coincides with the previously mentioned class. Moreover, it is demonstrated that every linear epsilon-free extended top-down tree transducer with regular look-ahead can be implemented by a linear multi bottom-up tree transducer. The class of transformations computed by the latter device is shown to be closed under composition, and to be included in the composition of the class of transformations computed by top-down tree transducers with itself. More precisely, it constitutes the composition closure of the class of transformations computed by finite-copying top-down tree transducers.