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 Sanjeev Arora, Boaz Barak - Cambridge University Press
The book provides an introduction to basic complexity classes, lower bounds on resources required to solve tasks on concrete models such as decision trees or circuits, derandomization and pseudorandomness, proof complexity, quantum computing, etc.
by Oded Goldreich - Cambridge University Press
The main focus of the current book is on the P-vs-NP Question and the theory of NP-completeness. Additional topics that are covered include the treatment of the general notion of a reduction between computational problems.
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 Martin Tompa
Lecture notes for a graduate course on computational complexity taught at the University of Washington. Alternating Turing machines are introduced very early, and deterministic and nondeterministic Turing machines treated as special cases.