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Autoreducibility, Mitoticity, and Immunity

  • Christian Glaßer
  • Mitsunori Ogihara
  • A. Pavan
  • Alan L. Selman
  • Liyu Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)

Abstract

We show the following results regarding complete sets.
  • NP-complete sets and PSPACE-complete sets are many-one autoreducible.

  • Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are many-one autoreducible.

  • EXP-complete sets are many-one mitotic.

  • NEXP-complete sets are weakly many-one mitotic.

  • PSPACE-complete sets are weakly Turing-mitotic.

  • If one-way permutations and quick pseudo-random generators exist, then NP-complete languages are m-mitotic.

  • If there is a tally language in NP ∩ coNP - P, then, for every ε > 0, NP-complete sets are not 2 n(1 + ε)-immune.

These results solve several of the open questions raised by Buhrman and Torenvliet in their 1994 survey paper on the structure of complete sets.

Keywords

Turing Machine SIAM Journal Regular Language Boolean Hierarchy Unconditional Result 
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 2005

Authors and Affiliations

  • Christian Glaßer
    • 1
  • Mitsunori Ogihara
    • 2
  • A. Pavan
    • 3
  • Alan L. Selman
    • 4
  • Liyu Zhang
    • 4
  1. 1.Universität Würzburg 
  2. 2.University of Rochester 
  3. 3.Iowa State University 
  4. 4.University at Buffalo 

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