Log-rank conjecture for XOR functions Since Log-rank conjecture appears too hard in its full generality,... let's try some special class of functions. ·XOR functions:f(x⊕y). --F=∫o⊕ The linear composition of x and y. Include important functions such as Equality, Hamming Distance,Gap Hamming Distance. Connection to Fourier:rank(M)=fLog-rank conjecture for XOR functions • Since Log-rank conjecture appears too hard in its full generality,… • let’s try some special class of functions. • XOR functions: 𝑓(𝑥 ⊕ 𝑦). --- 𝐹 = 𝑓 ∘⊕ – The linear composition of 𝑥 and 𝑦. – Include important functions such as Equality, Hamming Distance, Gap Hamming Distance. • Connection to Fourier: 𝑟𝑎𝑛𝑘 𝑀𝑓∘⊕ = 𝑓 መ 0