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The Dot-Depth and the Polynomial Hierarchy Correspond on the Delta Levels

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Developments in Language Theory (DLT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3340))

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Abstract

The leaf-language mechanism associates a complexity class to a class of regular languages. It is well-known that the Σ k - and Π k -levels of the dot-depth hierarchy and the polynomial hierarchy correspond in this formalism. We extend this correspondence to the Δ k -levels of these hierarchies: LeafP(Δ\(_{k}^{L}\)) = Δ\(_{k}^{p}\). These results are obtained in part by relating operators on varieties of languages to operators on the corresponding complexity classes.

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Author information

Authors and Affiliations

  1. Universität Tübingen, Germany

    Bernd Borchert, Klaus-Jörn Lange & Pascal Tesson

  2. National University of Singapore,  

    Frank Stephan

  3. McGill University, Montréal, Canada

    Denis Thérien

Authors
  1. Bernd Borchert
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  2. Klaus-Jörn Lange
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  3. Frank Stephan
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  4. Pascal Tesson
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  5. Denis Thérien
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, New Zealand

    Cristian S. Calude

  2. Computer Science, Institute of Information and Mathematical Sciences, Massey University Albany, Auckland, New Zealand

    Elena Calude

  3. Department of Computer Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Michael J. Dinneen

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© 2004 Springer-Verlag Berlin Heidelberg

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Borchert, B., Lange, KJ., Stephan, F., Tesson, P., Thérien, D. (2004). The Dot-Depth and the Polynomial Hierarchy Correspond on the Delta Levels. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_8

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  • DOI: https://doi.org/10.1007/978-3-540-30550-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24014-3

  • Online ISBN: 978-3-540-30550-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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