Lecture 18

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