The variable membership problem: Succinctness versus complexity

  • Gerhard Buntrock
  • Krzysztof LoryŚ
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Gerhard Buntrock
    • 1
  • Krzysztof LoryŚ
    • 2
  1. 1.Institut für InformatikUniversität WürzburgWürzburgGermany
  2. 2.Instytut InformatykiUniwersytet WroclawskiWroclawPoland

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