Theory of Computing ------------------- Title : Approximating the AND-OR Tree Authors : Alexander A. Sherstov Volume : 9 Number : 20 Pages : 653-663 URL : https://theoryofcomputing.org/articles/v009a020 Abstract -------- The _approximate degree_ of a Boolean function $f$ is the least degree of a real polynomial that approximates $f$ within $1/3$ at every point. We prove that the function $\bigwedge_{i=1}^n\bigvee_{j=1}^nx_{ij}$, known as the _AND-OR tree_, has approximate degree $\Omega(n)$. This lower bound is tight and closes a line of research on the problem, the best previous bound being $\Omega(n^{0.75})$. More generally, we prove that the function $\bigwedge_{i=1}^m\bigvee_{j=1}^nx_{ij}$ has approximate degree $\Omega(\sqrt{mn}),$ which is tight. The same lower bound was obtained independently by Bun and Thaler (2013) using related techniques.