Computational Complexity: A Modern Approach by Sanjeev Arora

››› Download audio book. ‹‹‹ Original Title: Computational Complexity ISBN: 0521424267 ISBN13: 9780521424264 Autor: Sanjeev Arora/Boaz Barak Rating: 3.9 of 5 stars (3864) counts Original Format: Hardcover, 579 pages Download Format: PDF, TXT, ePub, iBook. Published: May 1st 2009 / by Cambridge University Press / (first published December 13th 2007) Language:

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Description: This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

About Author: Other Editions:

- Computational Complexity: A Modern Approach (ebook)

- Computational Complexity: A Modern Approach (ebook)

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Rewiews:

Jun 22, 2009 Nick Black Rated it: really liked it Recommended to Nick by: Scott Aaronson via DJ Strouse Shelves: getoutofmydreams-andintomythesis, textbook-as-literature Amazon 2009-06-17. Wow, this is *REALLY GOOD* so far, definitely the best of several computational complexity books I've ever read (as the first major publishing event in complexity theory since Aaronson's development of the Complexity Zoo, perhaps there was a higher bar to leap). Seventeen thirty-two, personal note: my signature lifts a quote from the Complexity Zoo: Nondeterministic Polynomial-Time: The class of dashed hopes and idle dreams...The book was clearly designed with the assumption th Amazon 2009-06-17. Wow, this is *REALLY GOOD* so far, definitely the best of several computational complexity books I've ever read (as the first major publishing event in complexity theory since Aaronson's development of the Complexity Zoo, perhaps there was a higher bar to leap). Seventeen thirty-two, personal note: my signature lifts a quote from the Complexity Zoo: Nondeterministic Polynomial-Time: The class of dashed hopes and idle dreams...The book was clearly designed with the assumption that Sipser's modern classic Introduction to the Theory of Computation would be used as an undergraduate precursor; besides referencing Sipser several times early on (and his role heading up MIT's Math department, a group the authors are -- from the Foreward -- definitely good pals with (the authors themselves hail from Princeton, where I had no idea but Brian Kernighan and Robert Sedgewick are still faculty (of course I knew Andrew Appel, Edward Felten, and Robert Tarjan were still there, and Andrew Yao/Richard Lipton's emeritus status (but we've got Lipton now, motherfuckers!)))). The book takes off almost directly from where Sipser's study of complexity ends, with a deep study of p polynomial-time Karp reducibility (well, actually it starts with deterministic TM's, but as I've studied the 7-parameter TM formalism since I was thirteen or so, I didn't look at Chapter 1 too closely (I *do* applaud their Claim 1.6: single-tape simulation of k-tape TM's in time 5kT(n)^2 -- this kind of rigorous, strong presentation is welcomed -- and ESPECIALLY the early presentation of oblivious Turing Machines

(those which care only about the input length, not the input content), as this simplifies many a proof later on (most authors, if they introduce OTM's at all, do so only as a curiousity and not as a fundamental proof mechanism))). The heavy emphasis throughout on the dual miracles of randomization and modern crypto (including more advanced topics like derandomization, the probabilistic complexity classes, pseudorandomization and hardness amplification) will hopefully result in these topics being more deeply embedded within classical theory classes, as they should be. Furthermore, being placed (for the first time?) on the same footing as automata and the Hierarchy means that relevant issues are addressed throughout -- the implication that P == NP, for instance, would mean that nothing is to be gained from randomized algorithms, was entirely new to me *despite* having taken Lipton's Randomized Algorithms class and having read both of the two major books on the subject (Motwani + Raghavan and Mitzenmacher + Upfal). I can fairly say that realizing this obvious truth blew my mind. The book has wonderful quotes heading each chapter, which I just can't say enough about. Computer scientists don't know nearly enough of the rich history of their study (I'm regularly scandalized when I run into graduate students -- not the ladies and man-ladies in things like Human-Computer Interaction, but real apprentice computer scientists -- who don't know the names of Church, Rabin, Aho, Hamming and Hoare. I want to punch these ingrates in the face), and things like this can only help. The bibliography and citations are kind of sparse, but the important ones are there, and the authors are as current with the literature as one would hope (I was pleased to see the newly-seminal AKS2004 referenced early on). Be sure to check out section 2.7.3, "The P == NP Utopia", for a special treat -- coverage of the implications of that most foul heresy, the majority of which I'd heard elsewhere, but only as single, whispered perversions -- with a look forward to chapter 5, its coverage of the polynomial hierarchy, and a surprise or two regarding MIN-EQ-DNF (btw, if you've never read it, Aaronson's tongue-incheek "Polynomial Hierarchy Collapses" is one of the funniest things ever written). One comment -- the exercises, so far, are both really fucking weird and really fucking difficult. I am not sure I'd want to use this book's problem sets as self-study; classics like Papadimitriou are still the best in this arena, IMHO. I'm not yet done, and this might yet get its fifth star -- we'll see. What is certain, however, is that there is a new standard reference for undergraduate and graduate students, researchers and professionals interested in the majestic sweep of complexity theory, and its authors are Sanjeev Arora and Boaz Barak. 9 likes 22 comments