Depth-3 arithmetic formulae over fields of characteristic zero

Amir Shpilka*, Avi Wigderson

*Corresponding author for this work

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

Abstract

In this paper we prove near quadratic lower bounds for depth-3 arithmetic formulae over fields of characteristic zero. Such bounds are obtained for the elementary symmetric functions, the (trace of) iterated matrix multiplication, and the determinant. As corollaries we get the first non-trivial lower bounds for computing polynomials of constant degree, and a gap between the power depth-3 arithmetic formulas and depth-4 arithmetic formulas. The main technical contribution relates the complexity of computing a polynomial in this model to the wealth of partial derivatives it has on every affine subspace of small co-dimension. Lower bounds for related models utilize an algebraic analog of Nechiporuk lower bound on Boolean formulae.

Original languageEnglish
Title of host publicationProceedings of the Annual IEEE Conference on Computational Complexity
PublisherIEEE Comp Soc
Pages87-96
Number of pages10
ISBN (Print)0769500757
StatePublished - 1999
Externally publishedYes
EventProceedings of the 1999 14th Annual IEEE Conference on Computational Complexity - Atlanta, GA, USA
Duration: 4 May 19996 May 1999

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Conference

ConferenceProceedings of the 1999 14th Annual IEEE Conference on Computational Complexity
CityAtlanta, GA, USA
Period4/05/996/05/99

Fingerprint

Dive into the research topics of 'Depth-3 arithmetic formulae over fields of characteristic zero'. Together they form a unique fingerprint.

Cite this