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Compositions of Tree-to-Tree Statistical Machine Translation Models

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Developments in Language Theory (DLT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9840))

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Abstract

Compositions of well-known tree-to-tree translation models used in statistical machine translation are investigated. Synchronous context-free grammars are closed under composition in both the unweighted as well as the weighted case. In addition, it is demonstrated that there is a close connection between compositions of synchronous tree-substitution grammars and compositions of certain tree transducers because the intermediate trees can encode finite-state information. Utilizing these close ties, the composition closure of synchronous tree-substitution grammars is identified in the unweighted and weighted case. In particular, in the weighted case, these results build on a novel lifting strategy that will prove useful also in other setups.

Supported by the German Research Foundation (DFG) grant MA/4959/1-1.

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Notes

  1. 1.

    For technical reasons we disallow that \(\{t, t'\} \subseteq Q\).

  2. 2.

    Note that in an STSG the elements of \(\varSigma \) can label internal nodes and leaves.

  3. 3.

    For simplicity, we assume that nodes in different trees are disjoint.

  4. 4.

    Using only the weights 0 and 1.

  5. 5.

    A tree translation \(\tau :T_\varSigma (L) \times T_\varSigma (L) \rightarrow A\) is injective if for every output tree \(u \in T_\varSigma (L)\) there exists at most one input tree \(t \in T_\varSigma (L)\) such that \(\tau (t, u) \ne 0\).

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Authors and Affiliations

  1. Institute for Natural Language Processing, Universität Stuttgart, Pfaffenwaldring 5b, 70569, Stuttgart, Germany

    Andreas Maletti

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  1. Andreas Maletti
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Correspondence to Andreas Maletti .

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Editors and Affiliations

  1. Université du Québec à Montréal , Montreal, Québec, Canada

    Srečko Brlek

  2. Dept Mathematiques, Univ du Quebec Montreal Dept Mathematiques, Montreal, Québec, Canada

    Christophe Reutenauer

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Maletti, A. (2016). Compositions of Tree-to-Tree Statistical Machine Translation Models. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_24

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  • DOI: https://doi.org/10.1007/978-3-662-53132-7_24

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