Abstract Model complexity is a fundamental problem in deep learning. In this paper, we
conduct a systematic overview of the latest studies on model complexity in deep learning …

Boolean functions are perhaps the most basic objects of study in theoretical computer
science. They also arise in other areas of mathematics, including combinatorics, statistical …

This paper surveys recent results on the classification of discrete temporal properties, gives
an introduction to the methods that have been developed to obtain them, and explains the …

In this paper, we show that every (2^n-1+1)-vertex induced subgraph of the n-dimensional
cube graph has maximum degree at least n. This is the best possible result, and it improves …

This concise, accessible text provides a thorough introduction to quantum computing-an
exciting emergent field at the interface of the computer, engineering, mathematical and …

A fundamental objective of cryptography is to enable two persons to communicate over an
insecure channel (a public channel such as the internet) in such a way that any other person …

We examine the number of queries to input variables that a quantum algorithm requires to
compute Boolean functions on {0, 1} N in the black-box model. We show that the exponential …

Written by prominent experts in the field, this monograph provides the first comprehensive,
unified presentation of the structural, algorithmic and applied aspects of the theory of …

We discuss several complexity measures for Boolean functions: certificate complexity,
sensitivity, block sensitivity, and the degree of a representing or approximating polynomial …

Boolean circuit complexity is the combinatorics of computer science and involves many
intriguing problems that are easy to state and explain, even for the layman. This book is a …