Alexander Healy, Salil Vadhan, Emanuele Viola

We revisit the problem of hardness amplification in $\NP$, as

recently studied by O'Donnell (STOC `02). We prove that if $\NP$

has a balanced function $f$ such that any circuit of size $s(n)$

fails to compute $f$ on a $1/\poly(n)$ fraction of inputs, then

$\NP$ has a function $f'$ such ...
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Mark Braverman, Gil Cohen, Sumegha Garg

Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$, or to construct improved hitting sets, as ... more >>>

Eshan Chattopadhyay, Pooya Hatami, Omer Reingold, Avishay Tal

We present an explicit pseudorandom generator with seed length $\tilde{O}((\log n)^{w+1})$ for read-once, oblivious, width $w$ branching programs that can read their input bits in any order. This improves upon the work of Impaggliazzo, Meka and Zuckerman (FOCS'12) where they required seed length $n^{1/2+o(1)}$.

A central ingredient in our work ... more >>>

Raghu Meka, Omer Reingold, Avishay Tal

We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom generators with seed length $\tilde{O}(\log(n) \cdot \mathrm{poly}(1/\epsilon))$. This is the first improvement for pseudorandom generators fooling width $3$ ROBPs since the work ... more >>>