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International Symposium on Fundamentals of Computation Theory

FCT 2003: Fundamentals of Computation Theory pp 376–386Cite as

On the Exponentiation of Languages

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2751))

Abstract

We characterize the exponentiation of languages by other language operations: In the presence of some “weak” operations, exponentiation is exactly as powerful as complement and ε-free morphism. This characterization implies, besides others, that a semi-AFL is closed under complement iff it is closed under exponentiation. As an application we characterize the exponentiation closure of the context-free languages. Furthermore, P is closed under exponentiation iff P = NP , and NP is closed under exponentiation iff NP = co-NP.

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References

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Author information

Authors and Affiliations

  1. Institut für Algebra und Computermathematik, Technische Universität Wien, Wiedner Hauptstraße 8, A 1040, Wien

    Werner Kuich

  2. Institut für Informatik, Bayerische Julius-Maximilians-Universität Würzburg, Am Hubland, D-97074, Würzburg, Germany

    Klaus W. Wagner

Authors
  1. Werner Kuich
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  2. Klaus W. Wagner
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Lund University, 22100, Lund, Sweden

    Andrzej Lingas

  2. School of Technology and Society, Malmö University, SE-205 06, Malmö, Sweden

    Bengt J. Nilsson

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© 2003 Springer-Verlag Berlin Heidelberg

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Kuich, W., Wagner, K.W. (2003). On the Exponentiation of Languages. In: Lingas, A., Nilsson, B.J. (eds) Fundamentals of Computation Theory. FCT 2003. Lecture Notes in Computer Science, vol 2751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45077-1_35

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  • DOI: https://doi.org/10.1007/978-3-540-45077-1_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40543-6

  • Online ISBN: 978-3-540-45077-1

  • eBook Packages: Springer Book Archive

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