### 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.

Original language | English (US) |
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Pages (from-to) | 387-398 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science |

Volume | 3618 |

State | Published - Oct 24 2005 |

Externally published | Yes |

Event | 30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005 - Gdansk, Poland Duration: Aug 29 2005 → Sep 2 2005 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science*,

*3618*, 387-398.