We prove a new lower bound on the parity decision tree complexity $D_{\oplus}(f)$ of a Boolean function $f$. Namely, granularity of the Boolean function $f$ is the smallest $k$ such that all Fourier coefficients of $f$ are integer multiples of $1/2^k$. We show that $D_{\oplus}(f)\geq k+1$.

This lower bound is ... more >>>