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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- 1.
The ISI corpus is available at http://amr.isi.edu.
- 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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We thank the anonymous reviewers for their careful reading of our manuscript and their helpful comments.
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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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