In a previous post, the process of creating a fair coin from a biased coin was explored, leading to the realization that this is part of a larger problem of deterministic randomness extraction. The focus is on creating a stream of output bits that are uniformly random, despite potentially biased and correlated input bits. Various approaches are discussed, such as Von Neumann’s method and creating a parity extractor for input streams with varying biases. The concept of a Markov Chain input stream is also introduced, where the Blum extractor applies the Von Neumann rule to achieve randomness. Concluding that perfectly uniform bits cannot be achieved from a completely unknown input stream structure, statistical tests on the generated output are suggested for future exploration.
https://bytepawn.com/randomness-extractors-making-fair-coins-out-of-biased-coins.html