### Abstract

We show that there is a set which is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2lin. Here a set A in a complexity class C is almost complete for C under some reducibility r if the class of the problems in C which do not r-reduce to A has measure 0 in C in the sense of Lutz's resource-bounded measure theory. We also show that the almost complete sets for E under polynomial-time bounded one-one length-increasing reductions and truth-table reductions of norm 1 coincide with the almost p-m-complete sets for E. Moreover, we obtain similar results for the class EXP of sets computable in deterministic time 2^{poly}.

Original language | English (US) |
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Title of host publication | STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings |

Publisher | Springer Verlag |

Pages | 419-430 |

Number of pages | 12 |

ISBN (Print) | 9783540671411 |

State | Published - Jan 1 2000 |

Event | 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000 - Lille, France Duration: Feb 17 2000 → Feb 19 2000 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1770 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000 |
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Country | France |

City | Lille |

Period | 2/17/00 → 2/19/00 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings*(pp. 419-430). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1770). Springer Verlag.

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*STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1770, Springer Verlag, pp. 419-430, 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Lille, France, 2/17/00.

**Almost complete sets.** / Ambos-Spies, Klaus; Merkle, Wolfgang; Reimann, Jan Severin; Terwijn, Sebastiaan A.

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

TY - GEN

T1 - Almost complete sets

AU - Ambos-Spies, Klaus

AU - Merkle, Wolfgang

AU - Reimann, Jan Severin

AU - Terwijn, Sebastiaan A.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - We show that there is a set which is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2lin. Here a set A in a complexity class C is almost complete for C under some reducibility r if the class of the problems in C which do not r-reduce to A has measure 0 in C in the sense of Lutz's resource-bounded measure theory. We also show that the almost complete sets for E under polynomial-time bounded one-one length-increasing reductions and truth-table reductions of norm 1 coincide with the almost p-m-complete sets for E. Moreover, we obtain similar results for the class EXP of sets computable in deterministic time 2poly.

AB - We show that there is a set which is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2lin. Here a set A in a complexity class C is almost complete for C under some reducibility r if the class of the problems in C which do not r-reduce to A has measure 0 in C in the sense of Lutz's resource-bounded measure theory. We also show that the almost complete sets for E under polynomial-time bounded one-one length-increasing reductions and truth-table reductions of norm 1 coincide with the almost p-m-complete sets for E. Moreover, we obtain similar results for the class EXP of sets computable in deterministic time 2poly.

UR - http://www.scopus.com/inward/record.url?scp=84944081286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944081286&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540671411

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 419

EP - 430

BT - STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings

PB - Springer Verlag

ER -