The dot-depth and the polynomial hierarchy correspond on the delta levels

  • Authors:

  • Bernd Borchert;Klaus-Jörn Lange;Frank Stephan;Pascal Tesson;Denis Thérien

  • Affiliations:

  • Universität Tübingen, Germany;Universität Tübingen, Germany;National University of Singapore;Universität Tübingen, Germany;McGill University, Montréal, Canada

  • Venue:
  • DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
  • Year:
  • 2004

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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 Σk- and Πk-levels of the dot-depth hierarchy and the polynomial hierarchy correspond in this formalism. We extend this correspondence to the Δk-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.