Unbiased bits from sources of weak randomness and probabilistic communication complexity

A new model for weak random physical sources is presented. The new model strictly generalizes previous models. The sources considered output strings according to probability distributions in which no single string is too probable. The new model provides a fruitful viewpoint on problems studied previously such as: (1) extracting almost-perfect bits from sources of weak randomness; (2) probabilistic communication complexity; and (3) robustness of BPP with respect to sources of weak randomness.