Amir Shpilka, Avi Wigderson

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 nontrivial lower

bounds for ...
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Zohar Karnin, Amir Shpilka

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 ... more >>>

Nitin Saxena

Polynomial identity testing (PIT) is the problem of checking whether a given

arithmetic circuit is the zero circuit. PIT ranks as one of the most important

open problems in the intersection of algebra and computational complexity. In the last

few years, there has been an impressive progress on this ...
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Nitin Saxena, C. Seshadhri

We study the problem of identity testing for depth-3 circuits, over the

field of reals, of top fanin k and degree d (called sps(k,d)

identities). We give a new structure theorem for such identities and improve

the known deterministic d^{k^k}-time black-box identity test (Kayal &

Saraf, FOCS 2009) to one ...
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Nikhil Balaji, Nutan Limaye, Srikanth Srinivasan

In this note, we prove that there is an explicit polynomial in VP such that any $\Sigma\Pi\Sigma$ arithmetic circuit computing it must have size at least $n^{3-o(1)}$. Up to $n^{o(1)}$ factors, this strengthens a recent result of Kayal, Saha and Tavenas (ICALP 2016) which gives a polynomial in VNP with ... more >>>

Shuichi Hirahara

We establish an explicit link between depth-3 formulas and one-sided approximation by depth-2 formulas, which were previously studied independently. Specifically, we show that the minimum size of depth-3 formulas is (up to a factor of n) equal to the inverse of the maximum, over all depth-2 formulas, of one-sided-error correlation ... more >>>

Tameem Choudhury, Karteek Sreenivasaiah

The 2-Orthogonal Vectors (2-OV) problem is the following: given two tuples $A$ and $B$ of $n$ vectors each of dimension $d$, decide if there exists a vector $u\in A$, and $v\in B$ such that $u$ and $v$ are orthogonal. This problem, and its generalization $k$-OV defined analogously for $k$ tuples, ... more >>>