6 problems

Limiting Gotsman–Linial conjecture. The average sensitivity satisfies

Superweak Gotsman–Linial conjecture. For some function $g$ depending only on $d$,

Asymptotic Gotsman–Linial conjecture. There is an upper bound

Tight-upper-bound conjecture. The tight upper bound for the average sensitivity of any nested canalizing function is

Exact maximal-average-sensitivity conjecture. The maximal value of $s^f$ is

For an input $X=(x_1,x_2,\dots,x_n)\in\mathbb{Z}_2^n$, define $s(X)$ as the least positive representative of $\sum_{k=1}^n kx_k$ modulo $p$, with $1\leq s(X)\leq p$, and define the…