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The operators min and max on the polynomial hierarchy

  • Structural Complexity I
  • Conference paper
  • First Online:
STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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Abstract

Starting from Krentel's class OptP [Kre88] we define a general maximization operator max and a general minimization operator min for complexity classes and show that there are other interesting optimization classes beside OptP. We investigate the behavior of these operators on the polynomial hierarchy, in particular we study the inclusion structure of the classes max · P, max · NP, max · coNP, min · P, min · NP and min · coNP. Furthermore we prove some very powerful relations regarding the interaction of the operators max, min, U, Sig, C, ⊕, ∃ and ∀. This gives us a tool to show that the considered min and max classes are distinct under reasonable structural assumptions. Besides that, we are able to characterize the polynomial hierarchy uniformly by three operators.

A full version of this paper, including proofs of all claims, is available as Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, Technical Report Math/Inf/96/8.

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Authors and Affiliations

  1. Institut für Informatik, Friedrich-Schiller-Universität Jena, 07743, Jena

    Harald Hempel & Gerd Wechsung

Authors
  1. Harald Hempel
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  2. Gerd Wechsung
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Rüdiger Reischuk Michel Morvan

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© 1997 Springer-Verlag Berlin Heidelberg

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Hempel, H., Wechsung, G. (1997). The operators min and max on the polynomial hierarchy. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023451

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  • DOI: https://doi.org/10.1007/BFb0023451

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

  • eBook Packages: Springer Book Archive

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