Introduction to Complexity Theory
by Oded Goldreich
Number of pages: 375
Complexity Theory is a central field of Theoretical Computer Science, with a remarkable list of celebrated achievements as well as a very vibrant present research activity. The field is concerned with the study of the intrinsic complexity of computational tasks, and this study tend to aim at generality: It focuses on natural computational resources, and the effect of limiting those on the class of problems that can be solved. These lecture notes were taken by students attending my year-long introductory course on Complexity Theory, given in 1998-99 at the Weizmann Institute of Science. The course was aimed at exposing the students to the basic results and research directions in the field. The focus was on concepts and ideas, and complex technical proofs were avoided. It was assumed that students have taken a course in computability, and hence are familiar with Turing Machines.
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by Tim Roughgarden - Stanford University
The two biggest goals of the course are: 1. Learn several canonical problems that have proved the most useful for proving lower bounds; 2. Learn how to reduce lower bounds for fundamental algorithmic problems to communication complexity lower bounds.
by Oded Goldreich - Cambridge University Press
This book offers a comprehensive perspective to modern topics in complexity theory. It can be used as an introduction as either a textbook or for self-study, or to experts, since it provides expositions of the various sub-areas of complexity theory.
by Neil D. Jones - The MIT Press
The author builds a bridge between computability and complexity theory and other areas of computer science. Jones uses concepts familiar from programming languages to make computability and complexity more accessible to computer scientists.
by Luca Trevisan
Notes from a graduate courses on Computational Complexity. The first 15 lectures cover fundamentals, the remaining is advanced material: Hastad's optimal inapproximability results, lower bounds for parity in bounded depth-circuits, and more.