This beginning graduate textbook describes both recent achievements and classical results
of computational complexity theory. Requiring essentially no background apart from …

A complete treatment of fundamentals and recent advances in complexity theory Complexity
theory studies the inherent difficulties of solving algorithmic problems by digital computers …

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 …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

An historical overview of computational complexity is presented. Emphasis is on the
fundamental issues of defining the intrinsic computational complexity of a problem and …

and the Nature of Computer Science| n scientific work, the recognition by one's peers is one
of the greatest rewards. In particular, an official recognition by the scientific community, as …

This book is an accessible introduction to complexity theory and cryptology, two closely
related areas in theoretical computer science. Based on courses taught at Heinrich-Heine …

Just as the theory of computability had its foundations in the Church-Turing thesis,
computational complexity theory rests upon a modern strengthening of this thesis, which …

It all started with a machine. In 1936, Turing developed his theoretical computational model.
He based his model on how he perceived mathematicians think. As digital computers were …

This exposition is an introduction to the main ideas of Kolmogorov complexity and surveys
the wealth of useful applications of this elegant notion. We distinguish: I) Application of the …