### Abstract

Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question-whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all EXP-complete languages are polynomial-time length-decreasing self-reducible.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science |

Editors | J. Jedrzejowicz, A. Szepietowski |

Pages | 308-315 |

Number of pages | 8 |

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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*Lecture Notes in Computer Science*(Vol. 3618, pp. 308-315)

**Separating the notions of self- and autoreducibility.** / Faliszewski, Piotr; Ogihara, Mitsunori.

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

*Lecture Notes in Computer Science.*vol. 3618, pp. 308-315, 30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005, Gdansk, Poland, 8/29/05.

}

TY - GEN

T1 - Separating the notions of self- and autoreducibility

AU - Faliszewski, Piotr

AU - Ogihara, Mitsunori

PY - 2005

Y1 - 2005

N2 - Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question-whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all EXP-complete languages are polynomial-time length-decreasing self-reducible.

AB - Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question-whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all EXP-complete languages are polynomial-time length-decreasing self-reducible.

UR - http://www.scopus.com/inward/record.url?scp=26844460241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844460241&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:26844460241

VL - 3618

SP - 308

EP - 315

BT - Lecture Notes in Computer Science

A2 - Jedrzejowicz, J.

A2 - Szepietowski, A.

ER -