Autoreducibility, mitoticity, and immunity

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

Research output: Contribution to journalConference article

11 Scopus citations

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 2n(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.

Original languageEnglish (US)
Pages (from-to)387-398
Number of pages12
JournalLecture Notes in Computer Science
Volume3618
DOIs
StatePublished - 2005
Event30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005 - Gdansk, Poland
Duration: Aug 29 2005Sep 2 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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