Transcription of Computational Complexity: A Modern Approach
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Computational Complexity: A Modern Approach
DRAFTiComputational complexity : A ModernApproachDraft of a book : Dated January 2007 Comments welcome!Sanjeev Arora and Boaz BarakPrinceton to be reproduced or distributed without the authors permissionThis is an Internet draft. Some chapters are more finished than others. References andattributions are very preliminary and we apologize in advance for any omissions (but hope youwill nevertheless point them out to us).Please send us bugs, typos, missing references or general comments Thank You!!DRAFTiiDRAFTA bout this bookComputational complexity theory has developed rapidly in the past three decades. The list ofsurprising and fundamental results proved since 1990 alone could fill a book : these include newprobabilistic definitions of classical complexity classes (IP=PSPACEand thePCPT heorems)and their implications for the field of approximation algorithms; Shor s algorithm to factor integersusing a quantum computer; an understanding of why current approaches to the famousPversusNPwill not be successful; a theory of derandomization and pseudorandomness based upon com-putational hardness; and beautiful constructions of pseudorandom objects such as extractors book aims to describe such recent
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)
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