The coding theorem is a fundamental result of algorithmic information theory. A well known theorem of G´acs shows that the analog of the coding theorem fails for continuous sample...
We study the task of randomness extraction from sources which are distributed uniformly on an unknown algebraic variety. In other words, we are interested in constructing a functi...
—We study the one-way number-on-the-forhead (NOF) communication complexity of the k-layer pointer jumping problem. Strong lower bounds for this problem would have important impli...
—We show that the rank of a depth-3 circuit (over any field) that is simple, minimal and zero is at most O(k3 log d). The previous best rank bound known was 2O(k2 ) (log d)k−2...
We study the inapproximability of Vertex Cover and Independent Set on degree d graphs. We prove that: • Vertex Cover is Unique Games-hard to approximate to within a factor 2−(...