### 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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Title of host publication | Lecture Notes in Computer Science |

Editors | J. Jedrzejowicz, A. Szepietowski |

Pages | 387-398 |

Number of pages | 12 |

Volume | 3618 |

State | Published - 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 |

### Other

Other | 30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005 |
---|---|

Country | Poland |

City | Gdansk |

Period | 8/29/05 → 9/2/05 |

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Lecture Notes in Computer Science*(Vol. 3618, pp. 387-398)

**Autoreducibility, mitoticity, and immunity.** / Glaßer, Christian; Ogihara, Mitsunori; Pavan, A.; Selman, Alan L.; Zhang, Liyu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science.*vol. 3618, pp. 387-398, 30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005, Gdansk, Poland, 8/29/05.

}

TY - GEN

T1 - Autoreducibility, mitoticity, and immunity

AU - Glaßer, Christian

AU - Ogihara, Mitsunori

AU - Pavan, A.

AU - Selman, Alan L.

AU - Zhang, Liyu

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26844543338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844543338&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3618

SP - 387

EP - 398

BT - Lecture Notes in Computer Science

A2 - Jedrzejowicz, J.

A2 - Szepietowski, A.

ER -