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International Conference on Developments in Language Theory

DLT 2016: Developments in Language Theory pp 138–150Cite as

An Automata Characterisation for Multiple Context-Free Languages

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9840))

Abstract

We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.

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Notes

  1. 1.

    The control flow of our constructed automaton is similar to that of the treewalk evaluator for attribute grammars [8, Sect. 3]. The two major differences are that the treewalk evaluator also treats inherited attributes (which are not present in PMCFGs) and that our constructed automaton generates the tree on the fly (while the treewalk evaluator is already provided with the tree).

  2. 2.

    The k-MCFG \(G({\mathcal {M}})\) exists since \([\![\cdot ]\!]\) is a homomorphism and k-MCFLs are closed under homomorphisms [13, Theorem 3.9].

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, Technische Universität Dresden, Nöthnitzer Str. 46, 01062, Dresden, Germany

    Tobias Denkinger

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  1. Tobias Denkinger
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Correspondence to Tobias Denkinger .

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Editors and Affiliations

  1. Université du Québec à Montréal , Montreal, Québec, Canada

    Srečko Brlek

  2. Dept Mathematiques, Univ du Quebec Montreal Dept Mathematiques, Montreal, Québec, Canada

    Christophe Reutenauer

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Denkinger, T. (2016). An Automata Characterisation for Multiple Context-Free Languages. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_12

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  • DOI: https://doi.org/10.1007/978-3-662-53132-7_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53131-0

  • Online ISBN: 978-3-662-53132-7

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