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Composition Closure of Linear Extended Top-down Tree Transducers

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Abstract

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 ε-freeness, strictness, and nondeletion are considered. The composition hierarchy turns out to be finite for all ε-free (all rules consume input) variants of these transducers except for the nondeleting ε-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 ε-free transducers) the composition hierarchy does not collapse.

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Authors and Affiliations

  1. Leiden Institute of Advanced Computer Science, Leiden University, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

    Joost Engelfriet

  2. Department of Foundations of Computer Science, University of Szeged, Árpád tér 2, H-6720, Szeged, Hungary

    Zoltán Fülöp

  3. Institute of Computer Science, Universität Leipzig, Augustusplatz 10–11, 04109, Leipzig, Germany

    Andreas Maletti

Authors
  1. Joost Engelfriet
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  2. Zoltán Fülöp
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  3. Andreas Maletti
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Corresponding author

Correspondence to Andreas Maletti.

Additional information

This is a revised and extended version of [Z. Fülöp and A. Maletti: Composition closure of ε -free linear extended top-down tree transducers. In Proc. 17th DLT, volume 7907 of LNCS, pages 239–251. Springer-Verlag, 2013].

This work was partially supported by the exchange project 55 657 of the German Academic Exchange Service (DAAD) and Hungarian Scholarship Board Office (MÖB). Z. Fülöp was partially supported by the NKFI grant K 108 448, and A. Maletti was partially supported by the German Research Foundation (DFG) grant MA / 4959 / 1-1.

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Engelfriet, J., Fülöp, Z. & Maletti, A. Composition Closure of Linear Extended Top-down Tree Transducers. Theory Comput Syst 60, 129–171 (2017). https://doi.org/10.1007/s00224-015-9660-2

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