ON THE COMPLEXITY OF MATRIX GROUP PROBLEMS I.

Laszlo Babai, Endre Szemeredi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

117 Citations (Scopus)

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 languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherIEEE
Pages229-240
Number of pages12
ISBN (Print)081860591X
Publication statusPublished - 1984

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Babai, L., & Szemeredi, E. (1984). ON THE COMPLEXITY OF MATRIX GROUP PROBLEMS I. In Annual Symposium on Foundations of Computer Science (Proceedings) (pp. 229-240). IEEE.

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

Annual Symposium on Foundations of Computer Science (Proceedings). IEEE, 1984. p. 229-240.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Babai, L & Szemeredi, E 1984, ON THE COMPLEXITY OF MATRIX GROUP PROBLEMS I. in Annual Symposium on Foundations of Computer Science (Proceedings). IEEE, pp. 229-240.
Babai L, Szemeredi E. ON THE COMPLEXITY OF MATRIX GROUP PROBLEMS I. In Annual Symposium on Foundations of Computer Science (Proceedings). IEEE. 1984. p. 229-240
Babai, Laszlo ; Szemeredi, Endre. / ON THE COMPLEXITY OF MATRIX GROUP PROBLEMS I. Annual Symposium on Foundations of Computer Science (Proceedings). IEEE, 1984. pp. 229-240
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