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On weak growing context-sensitive grammars

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LATIN '95: Theoretical Informatics (LATIN 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 911))

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Abstract

We introduce the weak growing context-sensitive grammars (WGCSG): grammars that are growing with respect to a valuation of the positions inside a rule as well as the symbols. We evaluate a string by summing up every product of a symbol value with its position value. For every position valuation which does not agree with the beginning of any exponential function, the corresponding class of WGCSGs characterizes CSL. Such a valuation function is called unsteady. On the other hand all WGCSG related to steady position valuations are linearly inclusion-ordered and characterize the hierarchy of exponential time bounded languages in CSL. This hierarchy collapses iff.

  • any class defined by an unsteady position valuation has a normal form of order 2 (e. g. Cremers' or Kuroda's normal form)

  • any class defined by a steady position valuation is closed under inverse homomorphisms.

The results of our investigations first were developped in [Nie94]. Informations where the journal version will be published can be obtained via ftp/WWW service from haegar.informatik.uni-wuerzburg.de/pub/TRs/bunt-niem95.dvi.gz.

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Authors and Affiliations

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

    Gerhard Buntrock & Gundula Niemann

Authors
  1. Gerhard Buntrock
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  2. Gundula Niemann
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Editor information

Ricardo Baeza-Yates Eric Goles Patricio V. Poblete

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© 1995 Springer-Verlag Berlin Heidelberg

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Buntrock, G., Niemann, G. (1995). On weak growing context-sensitive grammars. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_88

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  • DOI: https://doi.org/10.1007/3-540-59175-3_88

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59175-7

  • Online ISBN: 978-3-540-49220-7

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