We prove a switching lemma for constant-depth circuits over the alphabet $F_p$ with generalized AND/OR gates, extending Tal's Fourier-analytic approach from the Boolean setting. The key new ingredient is a direct computation of the $L_1$ Fourier mass of AND/OR gates over $F_p$, which yields an exact closed-form expression for the ... more >>>

A major open problem at the interface of quantum computing and communication complexity is whether quantum protocols can be exponentially more efficient than classical protocols for computing total Boolean functions; the prevailing conjecture is that they are not. In a seminal work, Razborov (2002) resolved this question for AND-functions of ... more >>>

We study systems of linear equations modulo two in $n$ variables
with three variables in each equation. We assume that the system has
a solution with $pn$ variables taking the value 1 for some value
$00$ it is hard to find a solution
of the same weight that satisfies at ... more >>>