Lecture 9

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. $P$, $N{C}^0$, $N{C}^1\subseteq L\subseteq NL\subseteq N{C}^2$, matrix multiplication in $N{C}^1$, nonuniform $N{C}^1=$ poly-size formulas. Branching programs: non-uniform $L=$ poly-size branching programs, small-width branching programs, statement of Barrington's Theorem (nonuniform $N{C}^1=$ constant-width poly-size branching programs).