Any AND-OR Formula of Size $N$ Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
SIAM Journal on Computing
A generalization of spira's theorem and circuits with small segregators or separators
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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Some tradeoffs between the size and depth of algebraic formulas are shown. In particular, it is shown that, for any fixed $\epsilon 0$, any algebraic formula of size $S$ can be converted into an equivalent formula of depth $O(\log S)$ and size $O(S^{1+\epsilon})$. This result is an improvement over previously known results where, to obtain the same depth bound, the formula size is $\Omega(S^{\alpha})$, with~$\alpha \ge 2$.