Lower bounds for non-commutative computation

Noam Nisan*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

205 Scopus citations

Abstract

JVe consider algebraic computations which are not allowed to rely on the commut,at,ivity of multiplication. We obtain various lower bounds for algebraic formula size in this model: (1) Computing the determinant is as hard as computing the permanent and tight exponential upper and lower bounds are given. (2) Computation cannot be parallelized, as opposed to in the commutative case - this solves in the negative an open problem of hliller et al [8]. (3) The question of the power of negation in this model is shown to be closely related to a well known open problem relating communication complexity and rank. We then take modest steps towards extending our results to general, commutative algebraic computation, and prove exponential lower bounds for monotone algebraic circuit size, as well as for the size of certain types of constant depth algebraic circuits.

Original languageAmerican English
Title of host publicationProceedings of the 23rd Annual ACM Symposium on Theory of Computing, STOC 1991
PublisherAssociation for Computing Machinery
Pages410-418
Number of pages9
ISBN (Electronic)0897913973
DOIs
StatePublished - 3 Jan 1991
Event23rd Annual ACM Symposium on Theory of Computing, STOC 1991 - New Orleans, United States
Duration: 5 May 19918 May 1991

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F130073
ISSN (Print)0737-8017

Conference

Conference23rd Annual ACM Symposium on Theory of Computing, STOC 1991
Country/TerritoryUnited States
CityNew Orleans
Period5/05/918/05/91

Bibliographical note

Publisher Copyright:
© 1991 ACM.

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