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Computational Complexity: A Modern Approach Draft of a book: Dated January 2007 Comments welcome!
Sanjeev Arora and Boaz Barak Princeton University
[email protected]com
Not to be reproduced or distributed without the authors’ permission
This is an Internet draft. Some chapters are more finished than others. References and attributions are very preliminary and we apologize in advance for any omissions (but hope you will nevertheless point them out to us).
Please send us bugs, typos, missing references or general comments to
[email protected] — Thank You!!
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About this book Computational complexity theory has developed rapidly in the past three decades. The list of surprising and fundamental results proved since 1990 alone could fill a book: these include new probabilistic definitions of classical complexity classes (IP = PSPACE and the PCP Theorems) and their implications for the field of approximation algorithms; Shor’s algorithm to factor integers using a quantum computer; an understanding of why current approaches to the famous P versus NP will no