Highly Influenced

# Depth-3 arithmetic circuits over fields of characteristic zero

@article{Shpilka2001Depth3AC, title={Depth-3 arithmetic circuits over fields of characteristic zero}, author={Amir Shpilka and Avi Wigderson}, journal={computational complexity}, year={2001}, volume={10}, pages={1-27} }

- Published 2001 in computational complexity
DOI:10.1007/PL00001609

In this paper we prove quadratic lower bounds for depth-3 arithmetic circuits 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 nontrivial lower bounds for computing polynomials of constant degree, and a gap between the power of depth-3 arithmetic circuits and depth-4 arithmetic circuits. We also give new shorter formulae of constant depth for… CONTINUE READING

Highly Cited

This paper has 91 citations. REVIEW CITATIONS

#### From This Paper

##### Topics from this paper.

60 Citations

11 References

Similar Papers

#### Citations

##### Publications citing this paper.

#### Citation Statistics

#### 91 Citations

Citations per Year

Semantic Scholar estimates that this publication has

**91**citations based on the available data.See our **FAQ** for additional information.