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International Conference on Implementation and Application of Automata

CIAA 2017: Implementation and Application of Automata pp 27–39Cite as

On the Regularity and Learnability of Ordered DAG Languages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10329))

Abstract

Order-Preserving DAG Grammars (OPDGs) is a subclass of Hyper-Edge Replacement Grammars that can be parsed in polynomial time. Their associated class of languages is known as Ordered DAG Languages, and the graphs they generate are characterised by being acyclic, rooted, and having a natural order on their nodes. OPDGs are useful in natural-language processing to model abstract meaning representations. We state and prove a Myhill-Nerode theorem for ordered DAG languages, and translate it into a MAT-learning algorithm for the same class. The algorithm infers a minimal OPDG G for the target language in time polynomial in G and the samples provided by the MAT oracle.

J. Björklund—Supported by the Swedish Research Council, Grant No. 621-2012-4555.

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Notes

  1. 1.

    The ISI corpus is available at http://amr.isi.edu.

  2. 2.

    In [4], the grammars are called Restricted DAG Grammars, but we prefer to use a name that is more descriptive.

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Acknowledgments

We thank the anonymous reviewers for their careful reading of our manuscript and their helpful comments.

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Authors and Affiliations

  1. Department of Computing Science, Umeå University, Umeå, Sweden

    Henrik Björklund, Johanna Björklund & Petter Ericson

Authors
  1. Henrik Björklund
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  2. Johanna Björklund
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  3. Petter Ericson
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Corresponding author

Correspondence to Henrik Björklund .

Editor information

Editors and Affiliations

  1. LIGM (UMR 8049), CNRS, Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Arnaud Carayol

  2. LIGM (UMR 8049), Université Paris-Est, Marne-la-Vallée Cedex 2, France

    Cyril Nicaud

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Björklund, H., Björklund, J., Ericson, P. (2017). On the Regularity and Learnability of Ordered DAG Languages. In: Carayol, A., Nicaud, C. (eds) Implementation and Application of Automata. CIAA 2017. Lecture Notes in Computer Science(), vol 10329. Springer, Cham. https://doi.org/10.1007/978-3-319-60134-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-60134-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60133-5

  • Online ISBN: 978-3-319-60134-2

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