R1−ttSN(NP) distinguishes robust many-one and Turing completeness

  • Edith Hemaspaandra
  • Lane A. Hemaspaandra
  • Harald Hempel
Regular Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1203)


Do complexity classes have many-one complete sets if and only if they have Turing-complete sets? We prove that there is a relativized world in which a relatively natural complexity class—namely a downward closure of NP, R 1−tt SN (NP)—has Turing-complete sets but has no many-one complete sets. In fact, we show that in the same relativized world this class has 2-truth-table complete sets but lacks 1-truth-table complete sets. As part of the groundwork for our result, we prove that R 1−tt SN (NP) has many equivalent forms having to do with ordered and parallel access to NP and NP ∩ coNP.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Edith Hemaspaandra
    • 1
  • Lane A. Hemaspaandra
    • 2
  • Harald Hempel
    • 3
  1. 1.Department of MathematicsLe Moyne CollegeSyracuseUSA
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA
  3. 3.Inst. für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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