A matrix is blocky if it is a" blowup" of a permutation matrix. The blocky rank of a matrix M is
the minimum number of blocky matrices that linearly span M. Hambardzumyan, Hatami and …

A version of time-bounded Kolmogorov complexity, denoted KT, has received attention in
the past several years, due to its close connection to circuit complexity and to the Minimum …

We present an investigation on threshold circuits and other discretized neural networks in
terms of the following four computational resources—size (the number of gates), depth (the …

We consider the complexity of depth-three Boolean circuits with limited bottom fan-in that
compute some explicit functions. This is one of the simplest circuit classes for which we …

The evolution of the human brain was one of the milestones in the history of information after
the emergence of life. The underlying biological, chemical, and physical processes of the …

We survey the problem of covering and partitioning a bipartite graph using vertex-disjoint
unions of bicliques. The concept of a vertex-disjoint union of bicliques has been given many …

What sort of code is so difficult to analyze that every potential analyst can discern essentially
no information from the code, other than its input-output behavior? In their seminal work on …

In this paper, we investigate computational power of threshold circuits and other theoretical
models of neural networks in terms of the following four complexity measures: size (the …

One central aim of theoretical computer science is to understand the limits of computation.
On the one hand, algorithms give upper bounds on the resources required for a …