Tuesday, March 24, 2009

Lecture 18

Today we covered: Hardness vs. randomness corollaries of Nisan-Wigderson; Impagliazzo-Wigderson Theorem ($f \in \mathsf{E}$ requiring circuits of size $2^{\epsilon n}$ implies $\mathsf{P} = \mathsf{BPP}$); Hardness Amplification , $1 - 1/\mathrm{poly}(n)$ hardness to $1/2 + 1/\mathrm{poly}(n)$ hardness, with the XOR Lemma; Impagliazzo's proof via the Hard-Core Set Theorem (with Nisan's proof via the Minimax Theorem).

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