Ali Juma, Valentine Kabanets, Charles Rackoff, Amir Shpilka

For any given Boolean formula $\phi(x_1,\dots,x_n)$, one can

efficiently construct (using \emph{arithmetization}) a low-degree

polynomial $p(x_1,\dots,x_n)$ that agrees with $\phi$ over all

points in the Boolean cube $\{0,1\}^n$; the constructed polynomial

$p$ can be interpreted as a polynomial over an arbitrary field

$\mathbb{F}$. The problem ...
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Scott Aaronson, Avi Wigderson

Any proof of P!=NP will have to overcome two barriers: relativization

and natural proofs. Yet over the last decade, we have seen circuit

lower bounds (for example, that PP does not have linear-size circuits)

that overcome both barriers simultaneously. So the question arises of

whether there ...
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