Let $\cal C$ be a class of distributions over $\B^n$. A deterministic randomness extractor for $\cal C$ is a function $E:\B^n \ar \B^m$ such that for any $X$ in $\cal C$ the distribution $E(X)$ is statistically close to the uniform distribution. A long line of research deals with explicit constructions ... more >>>

We show that under a reasonable hardness assumptions, the time-bounded Kolmogorov distribution is a universal samplable distribution. Under the same assumption we exactly characterize the worst-case running time of languages that are in average polynomial-time over all P-samplable distributions.

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Explicit construction of Ramsey graphs or graphs with no large clique or independent set has remained a challenging open problem for a long time. While Erdos's probabilistic argument shows the existence of graphs on 2^n vertices with no clique or independent set of size 2n, the best known explicit constructions ... more >>>