List of Notation entry-wise multiplication of vectors the gradient:Vf(x)=(Dif(x),....Dnf(x)) > logical NOT 3 S3i is equivalent to ieS logical XOR (exclusive-or) (Eye度lfrP)p △ symmetric difference of sets;i.e.,SAT=i:i is in exactly one of S,T} logical OR A logical AND the convolution operator [z]F(z) coefficient on z in the power series F(z) 1A 0-1 indicator function for A 1B 0-1 indicator random variable for event B 24 the set of all subsets of A #a if a is a multi-index,denotes the number of nonzero com- ponents of a lal if a is a multi-index,denotes Liai ANDn the logical AND function on n bits:False unless all inputs are True A r:r.x=0 for all xeA) Aut(f) the group of automorphisms of Boolean function f xi进 Copyright@Ryan O'Donnell,2014.List of Notation ◦ entry-wise multiplication of vectors ∇ the gradient: ∇f (x) = (D1 f (x),...,Dn f (x)) ¬ logical NOT 3 S 3 i is equivalent to i ∈ S ⊕ logical XOR (exclusive-or) kˆ f kˆ p ( P γ∈❋cn 2 |fb(γ)| p ) 1/p 4 symmetric difference of sets; i.e., S4T = {i : i is in exactly one of S,T} ∨ logical OR ∧ logical AND ∗ the convolution operator [z k ]F(z) coefficient on z k in the power series F(z) 1A 0-1 indicator function for A 1B 0-1 indicator random variable for event B 2 A the set of all subsets of A #α if α is a multi-index, denotes the number of nonzero com￾ponents of α |α| if α is a multi-index, denotes P i αi ANDn the logical AND function on n bits: False unless all inputs are True A ⊥ {γ : γ· x = 0 for all x ∈ A} Aut(f ) the group of automorphisms of Boolean function f xiii Copyright © Ryan O’Donnell, 2014