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Lower Bound on Weights of Large Degree Threshold Functions
An integer polynomial of variables is called a \emph{threshold gate}
for a Boolean function of variables if for all x \in \zoon
if and only if . The \emph{weight} of a threshold gate is the sum
of its absolute values.
In this paper we study how large a weight might be needed if we fix some
function and some threshold degree. We prove lower bound
on this value. The best previous bound was (Podolskii,
2009).
In addition we present substantially simpler proof of the weaker
lower bound. This proof is conceptually similar to other
proofs of the bounds on weights of nonlinear threshold gates, but avoids a lot
of technical details arising in other proofs. We hope that this proof will help
to show the ideas behind the construction used to prove these lower bounds