Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Brandstädt, A., Wagner, K. Reversal bounded and visit bounded realtime computations. In Proc. FCT'83 (Ed. M. Karpinski), INCS 158 (1983)
Salomaa, A. Formal Languages, ACADEMIC PRESS, New York, San Francisco, London, 1973
Wechsung, G. The oscilation complexity and a hierarchy of context-free languages. In Proc. FCT'79 (Ed. L. Budach), Akademie-Verlag Berlin 1979, 508–515
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gundermann, T. (1985). A lower bound on the oscilation complexity of context-free languages. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028800
Download citation
DOI: https://doi.org/10.1007/BFb0028800
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15689-5
Online ISBN: 978-3-540-39636-9
eBook Packages: Springer Book Archive