Autoreducibility, mitoticity, and immunity

Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We show the following results regarding complete sets.•NP-complete sets and PSPACE-complete sets are polynomial-time many-one autoreducible.•Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are polynomial-time many-one autoreducible.•EXP-complete sets are polynomial-time many-one mitotic.•If there is a tally language in NP ∩ coNP - P, then, for every ε{lunate} > 0, NP-complete sets are not 2n (1 + ε{lunate})-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.

Original languageEnglish (US)
Pages (from-to)735-754
Number of pages20
JournalJournal of Computer and System Sciences
Issue number5
StatePublished - Aug 2007
Externally publishedYes


  • Autoreducibility
  • Complete sets
  • Immunity
  • Mitoticity
  • Weak mitoticity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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