2 problems

An intersection of $k$ halfspaces on $\mathbb{R}^n$ is a Boolean function $f:\mathbb{R}^n\to\{\pm1\}$ that equals $1$ exactly when all of its $k$ linear threshold functions equal…

Let a degree-$k$ polynomial threshold function (PTF) be a Boolean function of the form $f(x)=\operatorname{sign}(q(x))$, where $q:\mathbb{R}^n\to\mathbb{R}$ is a real degree-$k$ po…