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.

## Tuesday, April 7, 2009

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