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The join can lower complexity

  • Lane A. Hemaspaandra
  • Zhigen Jiang
  • Jörg Rothe
  • Osamu Watanabe
Session 7
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1090)

Abstract

We prove that the join of sets may actually be simpler than the sets themselves: there exist sets that are not in the second level of the extended low hierarchy [BBS86], EL2, yet their join is in EL2. That is, in terms of extended lowness, the join operator can lower complexity. We study the closure properties of EL2 and prove that EL2 is not closed under certain Boolean operations. To this end, we establish the first known (and optimal) EL2 lower bounds for certain notions generalizing Selman's P-selectivity [Sel79], which may be regarded as an interesting result in its own right.

Keywords

Polynomial Hierarchy Boolean Connective Extended Lowness Infinite Hierarchy Approximate Polynomial Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Lane A. Hemaspaandra
    • 1
  • Zhigen Jiang
    • 2
  • Jörg Rothe
    • 3
  • Osamu Watanabe
    • 4
  1. 1.Department of Computer ScienceUniversity of RochesterRochesterUSA
  2. 2.Institute of SoftwareChinese Academy of SciencesBeijingChina
  3. 3.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany
  4. 4.Department of Computer ScienceTokyo Institute of TechnologyTokyoJapan

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