On the power of chain rules in context free grammars

  • Norbert Blum
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 140)


For all n >- 2, we construct a context-free language Ln for which we prove the following:
  1. a)

    Ln has a cfg of size O(n)

  2. b)

    Any chain rule free cfg for Ln has size Ω(n log log n).



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  1. [H]
    Harrison, M.A.: Introduction to formal language theory, Addison-Wesley (1978)Google Scholar
  2. [Y]
    Yehudai, A.: On the complexity of grammer and language problems, Dissertation, Berkeley (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Norbert Blum
    • 1
  1. 1.Angewandte Mathematik und InformatikUniversität des SaarlandesSaarbrückenWest Germany

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