### Abstract

The following propositions are considered: (1) E = NE (i.e., it is decidable in exponential time whether there is a solution for an exponential-type search problem). (2) Every exponential-type search problem is solvable in exponential time. (3) The first solution to every exponential-type search problem can be found in exponential time. (4) E = E^{NP}. It is easy to see that (4) implies (3) implies (2) implies (1). It has been conjectured that the first and last of these assumptions are equivalent in every relativized world. It is proved here that there exist relativized words in which the last two implications are not reversible. This is evidence that the search problem is not reducible to decision problems in exponential time. It is also proved that the third and fourth assumptions are equivalent. The combinatorial core of the separation results is a lower bound on the parallel complexity of a generalized version of the X-search problem.

Original language | English |
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Title of host publication | Annual Symposium on Foundations of Computer Science (Proceedings) |

Publisher | Publ by IEEE |

Pages | 222-227 |

Number of pages | 6 |

ISBN (Print) | 0818619821 |

Publication status | Published - Nov 1989 |

Event | 30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA Duration: Oct 30 1989 → Nov 1 1989 |

### Other

Other | 30th Annual Symposium on Foundations of Computer Science |
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City | Research Triangle Park, NC, USA |

Period | 10/30/89 → 11/1/89 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science (Proceedings)*(pp. 222-227). Publ by IEEE.

**Decision versus search problems in super-polynomial time.** / Impagliazzo, Russell; Tardos, G.

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

*Annual Symposium on Foundations of Computer Science (Proceedings).*Publ by IEEE, pp. 222-227, 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 10/30/89.

}

TY - GEN

T1 - Decision versus search problems in super-polynomial time

AU - Impagliazzo, Russell

AU - Tardos, G.

PY - 1989/11

Y1 - 1989/11

N2 - The following propositions are considered: (1) E = NE (i.e., it is decidable in exponential time whether there is a solution for an exponential-type search problem). (2) Every exponential-type search problem is solvable in exponential time. (3) The first solution to every exponential-type search problem can be found in exponential time. (4) E = ENP. It is easy to see that (4) implies (3) implies (2) implies (1). It has been conjectured that the first and last of these assumptions are equivalent in every relativized world. It is proved here that there exist relativized words in which the last two implications are not reversible. This is evidence that the search problem is not reducible to decision problems in exponential time. It is also proved that the third and fourth assumptions are equivalent. The combinatorial core of the separation results is a lower bound on the parallel complexity of a generalized version of the X-search problem.

AB - The following propositions are considered: (1) E = NE (i.e., it is decidable in exponential time whether there is a solution for an exponential-type search problem). (2) Every exponential-type search problem is solvable in exponential time. (3) The first solution to every exponential-type search problem can be found in exponential time. (4) E = ENP. It is easy to see that (4) implies (3) implies (2) implies (1). It has been conjectured that the first and last of these assumptions are equivalent in every relativized world. It is proved here that there exist relativized words in which the last two implications are not reversible. This is evidence that the search problem is not reducible to decision problems in exponential time. It is also proved that the third and fourth assumptions are equivalent. The combinatorial core of the separation results is a lower bound on the parallel complexity of a generalized version of the X-search problem.

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UR - http://www.scopus.com/inward/citedby.url?scp=0024771883&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0818619821

SP - 222

EP - 227

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - Publ by IEEE

ER -