We analyze the Fourier growth, ie the L₁ Fourier weight at level k (denoted L_ {1, k}), of
read-once regular branching programs. We prove that every read-once regular branching …

In the coin problem we are asked to distinguish, with probability at least 2/3, between n\iid.
coins which are heads with probability 12+β from ones which are heads with probability 12 …

The level-k 1-Fourier weight of a Boolean function refers to the sum of absolute values of its
level-k Fourier coefficients. Fourier growth refers to the growth of these weights as k grows. It …

In this work we prove that there is a function f∈ E NP such that, for every sufficiently large n
and d=√ n/log n, fn (f restricted to n-bit inputs) cannot be (1/2+ 2− d)-approximated by F 2 …

Recently several conjectures were made regarding the Fourier spectrum of lowdegree
polynomials. We show that these conjectures imply new correlation bounds for functions …

For any n∈ ℕ and d= o (loglog (n)), we prove that there is a Boolean function F on n bits and
a value γ= 2− Θ (d) such that F can be computed by a uniform depth-(d+ 1) AC 0 circuit with …

In this note we compare two measures of the complexity of a class $\mathcal F $ of Boolean
functions studied in (unconditional) pseudorandomness: $\mathcal F $'s ability to distinguish …

The δ-Coin Problem is the problem of distinguishing between a sequence of coin tosses that
come up Heads with probability either 1+ δ/2 or 1− δ/2. The computational complexity of this …

Yao's XOR lemma states that for every function f:{0, 1}^ k→{0, 1}, if f has hardness 2/3 for
P/poly (meaning that for every circuit C in P/poly, Pr [C (X)= f (X)]≤ 2/3 on a uniform input X) …

Hegedűs's lemma is the following combinatorial statement regarding polynomials over finite
fields. Over a field F of characteristic p> 0 and for qa power of p, the lemma says that any …