This paper explores the previously studied measure called block number of Boolean functions, that counts the maximum possible number of minimal sensitive blocks for any input. We present close to tight upper bounds on the block number in terms of the function’s sensitivity and the allowed block size, improving previous ... more >>>

In this short expository note, we provide an introduction to a distribution testing (and, more generally, indistinguishability) lower bound method based on moment-matching via polynomials. This method, which underlies several of the tight lower bounds on estimating symmetric properties, had for many years appeared mysterious and near-magical to the ... more >>>

Proving super-linear lower bounds on the size of circuits computing explicit linear functions $A:{\mathbb {F}}^n \to {\mathbb {F}}^n$ is a fundamental long-standing open problem in circuit complexity. We focus on the case where ${\mathbb {F}}$ is a finite field. The circuit can be either a Boolean circuit or an arithmetic ... more >>>