Topics covered in Lecture 9:

Randomized space: $RL \subseteq BPL \subseteq L^{3/2}$ (Saks-Zhou Theorem), USTCON $\in RL$. Circuits (as parallel computation): $NC$ vs. $P$, $NC^0$, $NC^1 \subseteq L \subseteq NL \subseteq NC^2$, matrix multiplication in $NC^1$, nonuniform $NC^1 = $ poly-size formulas. Branching programs: non-uniform $L = $ poly-size branching programs, small-width branching programs, statement of Barrington's Theorem (nonuniform $NC^1 = $ constant-width poly-size branching programs).

## Thursday, February 12, 2009

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