Identity Testing for Depth-3 Circuits with Small Fan-in
نویسنده
چکیده
4 History of the Sylvester-Gallai Problem 6 4.1 Melchior’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.2 Motzkin’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 Kelly and Moser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.4 Green and Tao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 How to describe 3-color Sylvester-Gallai configurations? . . . . . . . . 8
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Black Box Polynomial Identity Testing of Depth-3 Arithmetic Circuits with Bounded Top Fan-in
In this paper we consider the problem of determining whether an unknown arithmetic circuit, for which we have oracle access, computes the identically zero polynomial. Our focus is on depth-3 circuits with a bounded top fan-in. We obtain the following results. 1. A quasi-polynomial time deterministic black-box identity testing algorithm for ΣΠΣ(k) circuits (depth-3 circuits with top fan-in equal...
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