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On the height of syntactical graphs

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Theoretical Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 104))

Abstract

Syntactical graphs are representations of derivations of arbitrary grammars. The height of syntactical graphs is introduced here as a complexity measure. It is shown that polynomial height-bounded e-free grammars are equivalent to polynomial time-bounded nondeterministic Turing machines, and that polynomial height-bounded arbitrary grammars are equivalent to polynomial space-bounded Turing machines. Furthermore, context-free languages are linear height-bounded and regular languages are logarithmic height-bounded, even for context-free grammars.

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Authors and Affiliations

  1. Institut für Informatik, Universität Bonn, Wegelerstr. 6, 5300, Bonn, West-Germany

    Franz-Josef Brandenburg

Authors
  1. Franz-Josef Brandenburg
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Peter Deussen

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© 1981 Springer-Verlag Berlin Heidelberg

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Brandenburg, FJ. (1981). On the height of syntactical graphs. In: Deussen, P. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017291

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  • DOI: https://doi.org/10.1007/BFb0017291

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10576-3

  • Online ISBN: 978-3-540-38561-5

  • eBook Packages: Springer Book Archive

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