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The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings x and y is dep(x, y) = max{C(x) - C(x | y), C(y) - C(y | x)}, where C(ċ) denotes the Kolmogorov complexity. It is shown that there exists a computable Kolmogorov extractor f such that, for any two n-bit strings with complexity s(n) and dependency α(n), it outputs a string of length s(n) with complexity s(n) - α(n) conditioned by any one of the input strings. It is proven that the above are the optimal parameters a Kolmogorov extractor can achieve. It is shown that independence amplification cannot be effectively realized. Specifically, if (after excluding a trivial case) there exist computable functions f1 and f2 such that dep(f1(x, y), f2(x, y)) ≤ β(n) for all n-bit strings x and y with dep(x, y) ≤ α(n), then β(n) ≥ α(n) - O(log n).