Lower Bounds on Testing Functions of Low Fourier Degree

We consider the problem of testing whether a Boolean function has Fourier degree $\leq k$ or it is $ε$-far from any Boolean function with Fourier degree $\leq k$. We improve the known lower bound of $Ω(k)$ \cite{BBM11,CGM10}, to $Ω(k/\sqrtε)$. The lower bound uses the recently discovered connections between property testing and communication complexity by Blais \textit{et. al.} \cite{BBM11}

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