Despite the widespread success of Transformers on NLP tasks, recent works have found
that they struggle to model several formal languages when compared to recurrent models …

The sensitivity of a Boolean function f is the maximum over all inputs x, of the number of
sensitive coordinates of x. The well-known sensitivity conjecture of Nisan (see also Nisan …

We provide new query complexity separations against sensitivity for total Boolean functions:
a power $3 $ separation between deterministic (and even randomized or quantum) query …

The Sensitivity Conjecture and the Log-rank Conjecture are among the most important and
challenging problems in concrete complexity. Incidentally, the Sensitivity Conjecture is …

Sensitivity, block sensitivity and certificate complexity are basic complexity measures of
Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially …

A natural measure of smoothness of a Boolean function is its sensitivity (the largest number
of Hamming neighbors of a point which differ from it in function value). The structure of …

We generalize and extend the ideas in a recent paper of Chiarelli, Hatami and Saks to prove
new bounds on the number of relevant variables for boolean functions in terms of a variety of …

The sensitivity conjecture of Nisan and Szegedy [CC'94] asks whether for any Boolean
function $ f $, the maximum sensitivity $ s (f) $, is polynomially related to its block sensitivity …

Various combinatorial/algebraic parameters are used to quantify the complexity of a
Boolean function. Among them, sensitivity is one of the simplest and block sensitivity is one …

The sensitivity of a Boolean function f:{0, 1}^ n->{0, 1} is the maximal number of neighbors a
point in the Boolean hypercube has with different f-value. Roughly speaking, the block …