A lower bound on the oscilation complexity of context-free languages

  • T. Gundermann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 199)


The paper deals with the oscilation complexity OSC introduced in [W 79] for context-free languages. It is known that CF \(CF \subseteq OSC\left( {log} \right)\) OSC(log), but it was an open question whether there exist context-free languages requiring logarithmic oscilation. We exhibit a language L ∈ CF for which a logarithmic lower bound on its oscilation complexity is established.

As a consequence we can conclude that the Dyck language D2 requires logarithmic oscilation.

Our proof method is a rather involved counting argument which exploits specific properties of L.


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  1. [BW 83]
    Brandstädt, A., Wagner, K. Reversal bounded and visit bounded realtime computations. In Proc. FCT'83 (Ed. M. Karpinski), INCS 158 (1983)Google Scholar
  2. [S 73]
    Salomaa, A. Formal Languages, ACADEMIC PRESS, New York, San Francisco, London, 1973Google Scholar
  3. [W 79]
    Wechsung, G. The oscilation complexity and a hierarchy of context-free languages. In Proc. FCT'79 (Ed. L. Budach), Akademie-Verlag Berlin 1979, 508–515Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • T. Gundermann
    • 1
  1. 1.Department of MathematicsFriedrich Schiller UniversityJena

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