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The variable membership problem: Succinctness versus complexity

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STACS 94 (STACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

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Abstract

A rule in a grammar is quasi growing if it is growing with respect to given weights of the symbols. Using this definition several types of grammars similar to context sensitive grammars are defined. In this paper we examine the variable membership problem for different types of grammars, namely context-sensitive grammars (CSG), quasi context-sensitive grammars (QCSG), growing context-sensitive grammars (GCSG), quasi growing context-sensitive grammars (QGCSG), and quasi growing grammars (QGG). We show the completeness of these problems in appropriate complexity classes (PSPACE, NEXPTIME). Interestingly the complexity of the variable membership problem differs even when the grammars define the same language class.

This research was partly supported by Humboldt Foundation.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Würzburg, D-97072, Würzburg, Germany

    Gerhard Buntrock

  2. Instytut Informatyki, Uniwersytet Wroclawski, 51-151, Wroclaw, Poland

    Krzysztof LoryŚ

Authors
  1. Gerhard Buntrock
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  2. Krzysztof LoryŚ
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Editor information

Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

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© 1994 Springer-Verlag Berlin Heidelberg

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Buntrock, G., LoryŚ, K. (1994). The variable membership problem: Succinctness versus complexity. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_174

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  • DOI: https://doi.org/10.1007/3-540-57785-8_174

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

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