All reports by Author Ragesh Jaiswal:

__
TR09-016
| 21st February 2009
__

Ilias Diakonikolas, Parikshit Gopalan, Ragesh Jaiswal, Rocco Servedio, Emanuele Viola#### Bounded Independence Fools Halfspaces

__
TR08-079
| 31st August 2008
__

Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets, Avi Wigderson#### Uniform Direct-Product Theorems: Simplified, Optimized, and Derandomized

Ilias Diakonikolas, Parikshit Gopalan, Ragesh Jaiswal, Rocco Servedio, Emanuele Viola

We show that any distribution on {-1,1}^n that is k-wise independent fools any halfspace h with error \eps for k = O(\log^2(1/\eps)/\eps^2). Up to logarithmic factors, our result matches a lower bound by Benjamini, Gurel-Gurevich, and Peled (2007) showing that k = \Omega(1/(\eps^2 \cdot \log(1/\eps))). Using standard constructions of k-wise ... more >>>

Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets, Avi Wigderson

The classical Direct-Product Theorem for circuits says

that if a Boolean function $f:\{0,1\}^n\to\{0,1\}$ is somewhat hard

to compute on average by small circuits, then the corresponding

$k$-wise direct product function

$f^k(x_1,\dots,x_k)=(f(x_1),\dots,f(x_k))$ (where each

$x_i\in\{0,1\}^n$) is significantly harder to compute on average by

slightly smaller ...
more >>>