Lecture 22

In this lecture we covered "derandomization implies circuit lower bounds" topics. In particular, we saw:

Kannan's Theorem, ${\Sigma }_2$ doesn't have fixed-polynomial size circuits.

The Babai-Fortnow-Lund Theorem, $EXP\subseteq P/poly\Rightarrow EXP=MA$, and its consequences: $MA$-$EXP$ does not have polynomial size circuits, derandomizing $MA$ to $NP$ implies showing $NEXP$ does not have polynomial size circuits.

Most of the Impagliazzo-Kabanets-Wigderson Theorem, $NEXP\subseteq P/poly\Rightarrow NEXP=EXP$ (and indeed $NEXP=MA$), along with Kabanets's "easy witness method". The remainder will be proved next time.