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Revision #1 to TR12-116 | 14th September 2012 18:54
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#### A Derandomized Switching Lemma and an Improved Derandomization of AC0

**Abstract:**
We describe a new pseudorandom generator for AC0. Our generator $\epsilon$-fools circuits of depth $d$ and size $M$ and uses a seed of length $\tilde O( \log^{d+4} M/\epsilon)$. The previous best construction for $d \geq 3$ was due to Nisan, and had seed length $O(\log^{2d+6} M/\epsilon)$.

A seed length of $O(\log^{2d + \Omega(1)} M)$ is best possible given Nisan-type generators and the current state of circuit lower bounds; Seed length $\Omega(\log^d M/\epsilon)$ is a barrier for any pseudorandom generator construction given the current state of circuit lower bounds. For $d=2$, a pseudorandom generator of seed length $\tilde O(\log^2 M/\epsilon)$ was known.

Our generator is based on a ``pseudorandom restriction'' generator which outputs restrictions that satisfy the conclusions of the Hastad Switching Lemma and that uses a seed of polylogarithmic length.

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TR12-116 | 13th September 2012 03:28
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#### A Derandomized Switching Lemma and an Improved Derandomization of AC0

**Abstract:**
We describe a new pseudorandom generator for AC0. Our generator $\epsilon$-fools circuits of depth $d$ and size $M$ and uses a seed of length $\tilde O( \log^{d+4} M/\epsilon)$. The previous best construction for $d \geq 3$ was due to Nisan, and had seed length $O(\log^{2d+6} M/\epsilon)$.

A seed length of $O(\log^{2d + \Omega(1)} M)$ is best possible given Nisan-type generators and the current state of circuit lower bounds; Seed length $\Omega(\log^d M/\epsilon)$ is a barrier for any pseudorandom generator construction given the current state of circuit lower bounds. For $d=2$, a pseudorandom generator of seed length $\tilde O(\log^2 M/\epsilon)$ was known.

Our generator is based on a ``pseudorandom restriction'' generator which outputs restrictions that satisfy the conclusions of the Hastad Switching Lemma and that uses a seed of polylogarithmic length.