### Abstract

Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the determinant is characterized by the complexity of counting the number of accepting computations of a nondeterministic logspace-bounded machine. (This class of functions is known as #L.) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of a theorem of Jung, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Annual Structure in Complexity Theory Conference |

Editors | Anon |

Publisher | Publ by IEEE |

Pages | 267-278 |

Number of pages | 12 |

ISBN (Print) | 0818656727 |

State | Published - 1994 |

Externally published | Yes |

Event | Proceedings of the 9th Annual Structure in Complexity Theory Conference - Amsterdam, Neth Duration: Jun 28 1994 → Jul 1 1994 |

### Other

Other | Proceedings of the 9th Annual Structure in Complexity Theory Conference |
---|---|

City | Amsterdam, Neth |

Period | 6/28/94 → 7/1/94 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the IEEE Annual Structure in Complexity Theory Conference*(pp. 267-278). Publ by IEEE.

**Relationships among PL, #L, and the determinant.** / Allender, Eric; Ogihara, Mitsunori.

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

*Proceedings of the IEEE Annual Structure in Complexity Theory Conference.*Publ by IEEE, pp. 267-278, Proceedings of the 9th Annual Structure in Complexity Theory Conference, Amsterdam, Neth, 6/28/94.

}

TY - GEN

T1 - Relationships among PL, #L, and the determinant

AU - Allender, Eric

AU - Ogihara, Mitsunori

PY - 1994

Y1 - 1994

N2 - Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the determinant is characterized by the complexity of counting the number of accepting computations of a nondeterministic logspace-bounded machine. (This class of functions is known as #L.) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of a theorem of Jung, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.

AB - Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the determinant is characterized by the complexity of counting the number of accepting computations of a nondeterministic logspace-bounded machine. (This class of functions is known as #L.) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of a theorem of Jung, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.

UR - http://www.scopus.com/inward/record.url?scp=0028599687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028599687&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0818656727

SP - 267

EP - 278

BT - Proceedings of the IEEE Annual Structure in Complexity Theory Conference

A2 - Anon, null

PB - Publ by IEEE

ER -