### Abstract

The authors construct a theory of black box groups, and apply it to matrix groups over finite fields. Elements of a black box group are encoded by strings of uniform length, and group operations are performed by an oracle. Subgroups are given by a list of generators. It is proved that for such subgroups, membership and divisor of the order are in NP**B (B the group box oracle). Under a plausible mathematical hypothesis on short presentations of finite simple groups, nonmembership and exact order will also be in NP**B and thus in the intersection of NP**B and coNP**B .

Original language | English |
---|---|

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

Publisher | IEEE |

Pages | 229-240 |

Number of pages | 12 |

ISBN (Print) | 081860591X |

Publication status | Published - 1984 |

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science (Proceedings)*(pp. 229-240). IEEE.

**ON THE COMPLEXITY OF MATRIX GROUP PROBLEMS I.** / Babai, Laszlo; Szemeredi, Endre.

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

*Annual Symposium on Foundations of Computer Science (Proceedings).*IEEE, pp. 229-240.

}

TY - GEN

T1 - ON THE COMPLEXITY OF MATRIX GROUP PROBLEMS I.

AU - Babai, Laszlo

AU - Szemeredi, Endre

PY - 1984

Y1 - 1984

N2 - The authors construct a theory of black box groups, and apply it to matrix groups over finite fields. Elements of a black box group are encoded by strings of uniform length, and group operations are performed by an oracle. Subgroups are given by a list of generators. It is proved that for such subgroups, membership and divisor of the order are in NP**B (B the group box oracle). Under a plausible mathematical hypothesis on short presentations of finite simple groups, nonmembership and exact order will also be in NP**B and thus in the intersection of NP**B and coNP**B .

AB - The authors construct a theory of black box groups, and apply it to matrix groups over finite fields. Elements of a black box group are encoded by strings of uniform length, and group operations are performed by an oracle. Subgroups are given by a list of generators. It is proved that for such subgroups, membership and divisor of the order are in NP**B (B the group box oracle). Under a plausible mathematical hypothesis on short presentations of finite simple groups, nonmembership and exact order will also be in NP**B and thus in the intersection of NP**B and coNP**B .

UR - http://www.scopus.com/inward/record.url?scp=0021550123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021550123&partnerID=8YFLogxK

M3 - Conference contribution

SN - 081860591X

SP - 229

EP - 240

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

PB - IEEE

ER -