Abstract
We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows: Let \(f : \mathbb {F}_2^n \rightarrow \lbrace -1, 1\rbrace\) be a Boolean function with Fourier support 𝒮 and Fourier sparsity k .
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