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Approximating Parikh Images for Generating Deterministic Graph Parsers

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Book cover Software Technologies: Applications and Foundations (STAF 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9946))

Abstract

The Parikh image of a word abstracts from the order of its letters. Parikh’s famous theorem states that the set of Parikh images of a context-free string language forms a semilinear set that can be effectively computed from its grammar. In this paper we study the computation of Parikh images for graph grammars defined by contextual hyperedge replacement (CHR). Our motivation is to generate efficient predictive top-down (PTD) parsers for a subclass of CHR grammars. We illustrate this by describing the subtask that identifies the nodes of the input graph that parsing starts with.

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Notes

  1. 1.

    Due to space restrictions, that paper describes only the HR case.

  2. 2.

    [n] denotes the set \(\{1, \dots , n\}\).

  3. 3.

    Note that a node with just a leaving \(\textit{goto}\) edge can actually not be a starting node although this is indicated by \(\psi ''(S^x_{\textsf {i}})\). The reason for this over-approximation is that rule \([\textsf {g}]_{x}\) can be be applied to \(D(\bullet )\) even if there is no additional node that could be used as a context node, which is actually necessary for applying CHR rule g.

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Acknowledgements

We thank the anonymous reviewers for the valuable comments.

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Authors and Affiliations

  1. Umeå Universitet, Umeå, Sweden

    Frank Drewes

  2. Universität Bremen, Bremen, Germany

    Berthold Hoffmann

  3. Universität der Bundeswehr München, Neubiberg, Germany

    Mark Minas

Authors
  1. Frank Drewes
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  2. Berthold Hoffmann
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  3. Mark Minas
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Corresponding author

Correspondence to Mark Minas .

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Editors and Affiliations

  1. Dipartimento di Informatica, Universita di Pisa, Pisa, Italy

    Paolo Milazzo

  2. Budapest University of Technology and Economics, Budapest, Hungary

    Dániel Varró

  3. Vienna University of Technology, Vienna, Austria

    Manuel Wimmer

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Drewes, F., Hoffmann, B., Minas, M. (2016). Approximating Parikh Images for Generating Deterministic Graph Parsers. In: Milazzo, P., Varró, D., Wimmer, M. (eds) Software Technologies: Applications and Foundations. STAF 2016. Lecture Notes in Computer Science(), vol 9946. Springer, Cham. https://doi.org/10.1007/978-3-319-50230-4_9

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  • DOI: https://doi.org/10.1007/978-3-319-50230-4_9

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  • Print ISBN: 978-3-319-50229-8

  • Online ISBN: 978-3-319-50230-4

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