An inequality for the Fourier spectrum of parity decision trees

Eric Blais, Li-Yang Tan, Andrew Wan

Abstract: We give a new bound on the sum of the linear Fourier coefficients of a Boolean function in terms of its parity decision tree complexity. This result generalizes an inequality of O'Donnell and Servedio for regular decision trees. We use this bound to obtain the first non-trivial lower bound on the parity decision tree complexity of the recursive majority function.