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In several settings, derandomization is known to follow from circuit lower bounds that themselves are equivalent to the existence of pseudorandom generators. This leaves open the question whether derandomization implies the circuit lower bounds that are known to imply it, i.e., whether the ability to derandomize in any way implies the ability to do so in… (More)

We present an alternate proof of the recent result by Gutfreund and Kawachi that derandom-izing Arthur-Merlin games into P NP implies linear-exponential circuit lower bounds for E NP. Our proof is simpler and yields stronger results. In particular, consider the promise-AM problem of distinguishing between the case where a given Boolean circuit C accepts at… (More)

This is a technical lecture throughout which we prove the hypercontractivity of the noise operator , a result that will be used in later lectures. The reader may wish to review the notes of lecture 6 for a discussion of the noise operator T α , the p-norm of a function from the Boolean cube to the reals, and the notion of hypercontractivity. (T α f)(x) = E… (More)

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