This book is rooted in the thesis that complexity theory is extremely rich in conceptual
content, and that this contents should be explicitly communicated in expositions and courses …

Previous literatures show that pre-trained masked language models (MLMs) such as BERT
can achieve competitive factual knowledge extraction performance on some datasets …

Simple parallel algorithms for the maximal independent set (MIS) problem are presented.
The first algorithm is a Monte Carlo algorithm with a very local property. The local property of …

One of the more significant achievements of twentieth century mathematics, especially from
the viewpoints of logic and computer science, was the work of Church, Gödel and Turing in …

A basic issue in computer science is the complexity of problems. Computational complexity
measures how much time or memory is needed as a function of the input problem size …

We show that any language recognized by an NC 1 circuit (fan-in 2, depth O (logn)) can be
recognized by a particular type of width 5 polynomial-size branching program. As any …

A new algorithm for finding a maximum matching in a general graph is presented; its special
feature being that the only computationally non-trivial step required in its execution is the …

The maturity of a field of research is probably best characterized by the existence of
handbooks that explain its problems, results, applications, and methodology; allow their …

In this paper we show that nondeterministic space s(n) is closed under complementation for
s(n) greater than or equal to \logn. It immediately follows that the context-sensitive …

We study the properties of small depth circuits. The main results are establishing lower
bounds on the size of small depth circuits computing functions such as parity and majority …