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Efficient Translation with Linear Bimorphisms

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Language and Automata Theory and Applications (LATA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10792))

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Abstract

We show that the image of a regular tree language under a linear bimorphism over binary signatures can be computed in linear time in the size of the input automaton. We do this by transformation into a novel normal form. Our result applies to the translation and parsing complexity of a wide range of grammar formalisms used in computational linguistics, which can now be shown in a uniform way.

We thank Frank Drewes, Meaghan Fowlie, Jonas Groschwitz, Andreas Maletti, and Heiko Vogler for discussions about the paper and the anonymous reviewers for their feedback. This work was supported by DFG grant KO 2916/2-1.

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Notes

  1. 1.

    Recall that \(\mathop {{\textsf {ar}}}(r_0) \in \{0,1,2\}\): we use sequences to avoid distinguishing between cases.

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Authors and Affiliations

  1. Department of Language Science and Technology, Saarland University, Campus C7.2, Saarbrücken, Germany

    Christoph Teichmann, Antoine Venant & Alexander Koller

Authors
  1. Christoph Teichmann
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  2. Antoine Venant
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  3. Alexander Koller
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Corresponding author

Correspondence to Antoine Venant .

Editor information

Editors and Affiliations

  1. Bar-Ilan University, Ramat Gan, Israel

    Shmuel Tomi Klein

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. Ariel University, Ariel, Israel

    Dana Shapira

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Teichmann, C., Venant, A., Koller, A. (2018). Efficient Translation with Linear Bimorphisms. In: Klein, S., Martín-Vide, C., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2018. Lecture Notes in Computer Science(), vol 10792. Springer, Cham. https://doi.org/10.1007/978-3-319-77313-1_24

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  • DOI: https://doi.org/10.1007/978-3-319-77313-1_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77312-4

  • Online ISBN: 978-3-319-77313-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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