Depth-3 arithmetic circuits over fields of characteristic zero

  title={Depth-3 arithmetic circuits over fields of characteristic zero},
  author={Amir Shpilka and Avi Wigderson},
  journal={computational complexity},
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
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Private communication

  • M. Ben-Or
  • 1999
Highly Influential
6 Excerpts

A Boolean function

  • E. I. Nečiporuk
  • Soviet Math. Dokl. 7, 999–1000.
  • 1966
Highly Influential
4 Excerpts

The complexity of partial derivatives

  • V. Strassen
  • Theoret . Comput . Sci .
  • 1983
Highly Influential
3 Excerpts

Lower bounds on the size of bounded depth circuits over a complete basis with logical addition

  • A. A. Razborov
  • Math. Notes 41, 333–338.
  • 1987
2 Excerpts

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