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Summary: Com S 633: Randomness in Computation
Lecture 21 Scribe: Aaron Sterling
Today's Topic: Pseudo-Random Distributions.
Throughout, X will be a probability distribution over n and U will be
the uniform distribution over n .
Intuitively, how do we check that X = U? We do a statistical test on
elements of n produced by X, and see whether the behavior is uniform. For
example, is the parity zero 50% of the time, and one the other 50% of the
time? X \passes" a statistical test if the outcome of the test is \close" to
what the outcome would be if the test were performed on U .
Formally, a test will be a function Test : n ! f0; 1g. We then look at
the size of the di erence
Pr
x2U
[Test(x) = 1] Pr
x2X
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