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Kernels of Sub-classes of Context-Free Languages

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SOFSEM 2020: Theory and Practice of Computer Science (SOFSEM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12011))

Abstract

While the closure of a language family \(\mathscr {L}\) under certain language operations is the least family of languages which contains all members of \(\mathscr {L}\) and is closed under all of the operations, a kernel of \(\mathscr {L}\) is a greatest family of languages which is a subfamily of \(\mathscr {L}\) and is closed under all of the operations. Here we investigate properties of kernels of general language families and operations defined thereon as well as kernels of (deterministic) (linear) context-free languages with a focus on Boolean operations. While the closures of language families usually are unique, this uniqueness is not obvious for kernels. We consider properties of language families and operations that yield unique and non-unique, that is a set, of kernels. For the latter case, the question whether the union of all kernels coincides with the language family, or whether there are languages that do not belong to any kernel is addressed. Furthermore, the intersection of all kernels with respect to certain operations is studied in order to identify sets of languages that belong to all of these kernels.

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Acknowledgment

The author would like to thank Henning Fernau for fruitful discussions at an early stage of the paper.

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib

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  1. Martin Kutrib
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Correspondence to Martin Kutrib .

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Editors and Affiliations

  1. University of Macedonia, Thessaloniki, Greece

    Alexander Chatzigeorgiou

  2. University of Bergamo, Bergamo, Italy

    Riccardo Dondi

  3. Cyprus University of Technology, Limassol, Cyprus

    Herodotos Herodotou

  4. Carnegie Mellon University Qatar, Doha, Qatar

    Christos Kapoutsis

  5. Open University of Cyprus, Nicosia, Cyprus

    Yannis Manolopoulos

  6. University of Cyprus, Nicosia, Cyprus

    George A. Papadopoulos

  7. Paris Dauphine University, Paris, France

    Florian Sikora

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Kutrib, M. (2020). Kernels of Sub-classes of Context-Free Languages. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_12

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  • DOI: https://doi.org/10.1007/978-3-030-38919-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38918-5

  • Online ISBN: 978-3-030-38919-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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