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

Every boolean function may be represented as a real polynomial. In this paper we
characterize the degree of this polynomial in terms of certain combinatorial properties of the …

For Boolean functions f:{0, 1} n->{0, 1} and g:{0, 1} m->{0, 1}, the function composition of f
and g denoted by f O g:{0, 1} nm->{0, 1} is the value of f on n inputs, each of them is the …

Every Boolean function may be represented as a real polynomial. In this paper, we
characterize the degree of this polynomial in terms of certain combinatorial properties of the …

Before there was computer science, there was Boolean complexity. A hundred years ago,
logicians tried to find the smallest formulae for logical statements. Finding the smallest …

In the last decade substantial progress has been made in our understanding of restricted
classes of Boolean circuits, in particular those restricted to have constant depth (Furst …

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 …

In 1986, Saks and Wigderson conjectured that the largest separation between deterministic
and zero-error randomized query complexity for a total Boolean function is given by the …

This paper gives a full characterization of the time needed to compute a Boolean function on
a CREW PRAM with an unlimited number of processors. The characterization is given in …

The Boolean Decision tree model is perhaps the simplest model that computes Boolean
functions; it charges only for reading an input variable. We study the power of randomness …