## Polynomial identity testing for depth 3 circuits (2006)

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by
Neeraj Kayal
,
Shubhangi Saraf

Venue: | in Proceedings of the twenty-first Annual IEEE Conference on Computational Complexity (CCC |

Citations: | 23 - 5 self |

### BibTeX

@INPROCEEDINGS{Kayal06polynomialidentity,

author = {Neeraj Kayal and Shubhangi Saraf},

title = {Polynomial identity testing for depth 3 circuits},

booktitle = {in Proceedings of the twenty-first Annual IEEE Conference on Computational Complexity (CCC},

year = {2006}

}

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### Abstract

Abstract — We study ΣΠΣ(k) circuits, i.e., depth three arithmetic circuits with top fanin k. We give the first deterministic polynomial time blackbox identity test for ΣΠΣ(k) circuits over the field Q of rational numbers, thus resolving a question posed by Klivans and Spielman (STOC 2001). Our main technical result is a structural theorem for ΣΠΣ(k) circuits that compute the zero polynomial. In particular we show that if a ΣΠΣ(k) circuit C = ∑ i∈[k] Ai