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Towards a 2-Multiple Context-Free Grammar for the 3-Dimensional Dyck Language

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At the Intersection of Language, Logic, and Information (ESSLLI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11667))

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Abstract

We discuss the open problem of parsing the Dyck language of 3 symbols, \(D^3\), using a 2-Multiple Context-Free Grammar. We attempt to tackle this problem by implementing a number of novel meta-grammatical techniques and present the associated software packages we developed.

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Notes

  1. 1.

    https://github.com/omelkonian/dyck.

  2. 2.

    An avid reader will notice the use of the \(\mathcal {O}\) meta-rule in the ARIS algorithm.

  3. 3.

    https://oeis.org/A000108.

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Acknowledgements

We would like to thank Michael Moortgat for introducing us to the problem, providing insightful feedback and motivating us throughout the process, as well as Jurriaan Hage for suggesting the use of multi-dimensional Dyck languages in static program analysis.

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Authors and Affiliations

  1. Utrecht University, Utrecht, The Netherlands

    Konstantinos Kogkalidis & Orestis Melkonian

Authors
  1. Konstantinos Kogkalidis
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  2. Orestis Melkonian
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Corresponding author

Correspondence to Orestis Melkonian .

Editor information

Editors and Affiliations

  1. Universität Stuttgart, Stuttgart, Germany

    Jennifer Sikos

  2. Department of Philosophy, University of Maryland, College Park, MD, USA

    Eric Pacuit

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Kogkalidis, K., Melkonian, O. (2019). Towards a 2-Multiple Context-Free Grammar for the 3-Dimensional Dyck Language. In: Sikos, J., Pacuit, E. (eds) At the Intersection of Language, Logic, and Information. ESSLLI 2018. Lecture Notes in Computer Science(), vol 11667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59620-3_5

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  • DOI: https://doi.org/10.1007/978-3-662-59620-3_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-59619-7

  • Online ISBN: 978-3-662-59620-3

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