Bounded independence plus noise

• Online Access: http://hdl.handle.net/2047/D20321694

Derandomization is a fundamental research area in theoretical computer science. In the past decade, researchers have been able to derandomize a number of computational problems, leading to breakthrough discoveries such as proving SL=L, explicit constructions of Ramsey graphs and optimal-rate error-correcting codes. Bounded independent and small-bias distributions are two pseudorandom primitives that are used extensively in derandomization. This thesis studies the power of these primitives under the perturbation of noise. We give positive and negative results on these perturbed distributions. In particular, we show that they are significantly more powerful than the unperturbed ones, and have the potential to solve long standing open problems such as proving RL=L and AC^0[+] lower bounds. As applications, we give new lower bounds on the complexity of decoding error-correcting codes, nearly-optimal pseudorandom generators for old and new classes of tests, and limitations on the sum of small-bias distributions.