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Computational Complexity

A Conceptual Perspective

Complexity Theory is a central ﬁeld of the theoretical foundations of computer science.

It is concerned with the general study of the intrinsic complexity of computational tasks;

that is, it addresses the question of what can be achieved within limited time (and/or with

other limited natural computational resources).

This book offers a conceptual perspective on Complexity Theory. It is intended to serve

as an introduction for advanced undergraduate and graduate students, either as a textbook

or for self-study. The book will also be useful to experts, since it provides expositions of

the various sub-areas of Complexity Theory such as hardness ampliﬁcation, pseudoran-

domness, and probabilistic proof systems.

In each case, the author starts by posing the intuitive questions that are addressed by the

sub-area and then discusses the choices made in the actual formulation of these questions,

the approaches that lead to the answers, and the ideas that are embedded in these answers.

Oded Goldreich is a Professor of Computer Science at the Weizmann Institute of Science

and an Incumbent of the Meyer W. Weisgal Professorial Chair. He is an editor for the

SIAM Journal on Computing,

the

Journal of Cryptology,

and

Computational Complex-

ity

and previously authored the books

Modern Cryptography, Probabilistic Proofs and

Pseudorandomness,

and the two-volume work

Foundations of Cryptography.

Computational Complexity

A Conceptual Perspective

Oded Goldreich

Weizmann Institute of Science