### 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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Pages (from-to) | 308-315 |

Number of pages | 8 |

Journal | Lecture Notes in Computer Science |

Volume | 3618 |

DOIs | |

State | Published - 2005 |

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science*,

*3618*, 308-315. https://doi.org/10.1007/11549345_27