Randomness is Linear in Space

We show that any randomized algorithm that runs in spaceSand timeTand uses poly(S) random bits can be simulated using onlyO(S) random bits in spaceSand timeT+poly(S). A deterministic simulation in spaceSfollows. Of independent interest is our main technical tool: a procedure which extracts randomness from a defective random source using a small additional number of truly random bits.

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