Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity

Abstract

A new model for weak random physical sources is presented. The new model strictly generalizes previous models (e.g. the Santha and Vazirani model [26]). 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 as: 1) Extracting almost perfect bits from sources of weak randomness: the question of possibility as well as the question of efficiency of such extraction schemes are addressed. 2) Probabilistic Communication Complexity: it is shown that most functions have linear communication complexity in a very strong probabilistic sense. 3) Robustness of BPP with respect to sources of weak randomness (generalizing a result of Vazirani and Vazirani [29]).