We consider the problem of estimating the average of a huge set of values. That is, given oracle access to an arbitrary function $f:\{0,1\}^n\mapsto[0,1]$, we need to estimate $2^{-n} \sum_{x\in\{0,1\}^n} f(x)$ upto an additive error of $\epsilon$. We are allowed to employ a randomized algorithm which may err with probability ... more >>>

In this work we show that Unique k-SAT is as Hard as k-SAT for every $k \in {\mathds N}$. This settles a conjecture by Calabro, Impagliazzo, Kabanets and Paturi \cite{CIKP03}. To provide an affirmative answer to this conjecture, we develop a randomness optimal construction of Isolation Lemma(see Valiant and Vazirani ... more >>>

We initiate a general study of the randomness complexity of property testing, aimed at reducing the randomness complexity of testers without (significantly) increasing their query complexity. One concrete motovation for this study is provided by the observation that the product of the randomness and query complexity of a tester determine ... more >>>