Computational Complexity: A Modern Approach. Sanjeev Arora and Boaz Barak. Princeton University Authors: Sanjeev Arora, Princeton University, New Jersey; Boaz Barak, both recent achievements and classical results of computational complexity theory. Computational Complexity: A. Modern Approach. Draft of a book: Dated August Comments welcome! Sanjeev Arora and Boaz Barak. Princeton University.

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Student and researchers alike ccomplexity find it to be an immensely useful resource. This book contains essentially all of the many exciting developments of the last two decades, with high level intuition and detailed technical proofs. It is a must for everyone interested in this field. It will serve the needs com;utational a wide audience, ranging from experienced researchers to graduate students and ambitious undergraduates seeking an introduction to the mathematical foundations of computer science.

### Computational Complexity: A Modern Approach / Sanjeev Arora and Boaz Barak

I will keep it at my side as a useful reference for my own teaching and research. Karp, University Professor, University of California at Berkeley “The reviewer’s impressions are that this new textbook on computational complexity is available for a very attractive price and that on Amazon it may be verified that it has received very good reviews by several leaders in this field Karp, Sipser, Wigderson. This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory, including interactive proofs, PCP, derandomization, and quantum computation.

It can be used as a reference, for self-study, or as a textbook. More than exercises are included. Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support?

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.

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Customers who bought this item also bought. Page 1 of 1 Start over Page 1 of 1. Introduction to the Theory of Computation. The Nature of Computatuonal. Review “This text is a major achievement that brings together all of the important developments in complexity theory.

Cambridge University Press; 1 edition April 20, Language: Start reading Aroga Complexity: A Modern Approach on your Kindle in under a minute. Don’t have a Kindle? Try the Kindle edition and experience these great reading features: Is this coomputational helpful? Thank you for your feedback. Share your thoughts with other customers. Write a customer review. Read reviews that mention computational complexity computer science complexity theory kindle version quantum computing turing machine subject matter arora and barak mathematical background interactive proofs read this book complexity classes good book complexity textbook chapter textbook math text authors cryptography.

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There was a problem filtering reviews complfxity now. Please try again later. This is a very comprehensive text containing many results. However the complwxity of typos is astounding, and when appearing in the middle of a proof, it often takes a lot of extra effort on the part of the reader to figure out if there is some subtlety afoot or if it’s just a dumb copy-paste error that made it past the editor.

For example, the proof of Savitch’s theorem begins as follows: As compuattional turns out, yes. What’s more, the bwrak in general are very difficult to follow, but it’s my computationa, that this is in part just the style of the material, so this isn’t factored into my 3 star review. However, on more than one occasion I’ve seen much more elegant approaches to some of the proofs here nicer reductions, etc that make life a lot nicer. In future editions it would be nice to see some effort going into making the proofs more elegant and getting rid of the gross amount of typos.

A math text should NOT leave the reader wondering if the proof that they just read is actually valid. I trust the statements of the theorems but after almost pages computatlonal reading I have learned almost nothing about how to actually prove them. To end on a positive note, the motivation behind a lot of the text is very nice, and with some cleaning up this could easily be a 5 star review.

Further, there are no other texts trying to do what Arora and Barak are doing namely, compiling all modern results in Complexity Theorymaking this a very valuable resource. I may start looking at original material and using this as a source to structure the theory at a high level, leaving lower level verification to other sources – from that point of view, this text is very well suited.

Wish Computationwl could rate this higher, I really want to like it! I downloaded a sample of this for my kindle. I was really disapointed to find that the math did not look good at all on the kindle’s screen.

I will probably not buy any technical books until the math font set is improoved. Kindle version is terrible.

Kindle Edition Verified Purchase. I find this book readable until there are mathematical statements like this definition: Computahional every function T: I wish that such statements were accompanied by a conversational English translation.

### CSCI – Computational Complexity | Fall

Otherwise the English is quite readable. Coomputational Kindle version has difficulty with the notation, which makes me recommend against.

The Bookerly font displays most of the symbols correctly, but chokes on lower-case phi, among others. Worse, negation bars don’t appear at all, so the thing is just an exercise in frustration. The other fonts are utterly useless, with broken symbols all over some pages – but at least you won’t get fooled. This does not remind me of the quote by Peter Peterson speaking of one of his own books, “Once you put it down you won’t be able to pick it up.

## Computational Complexity: A Modern Approach

There are shades of Bertrand Russell yielding the floor to Ludwig Wittgenstein. But there are excellent aspects to this book and I am glad I dived in. N obody was able to aroea that their systems are simultaneously complete i. InKurt Godel shocked the mathematical world by showing that this ongoing effort was doomed to fail The focus of the book seems to turn on this issue of the CT thesis. So there is an argument central to the book rather then just a nice step by step presentation.

An interesting explanation of the difference is in “Recognizing the correctness of an answer is often much easier than coming up with the answer. Godel remains relevant to this as this turns out to be a version of his “Entscheidungsproblem”. They could all be replaced by machines.

## CSCI 7000-005: Computational Complexity

By the way, I read into all of this a concern with natural languages as well since I am convinced they are the same sort of complex systems at issue, so these can all apply to issues regarding the arts and translation and so on. I gather they are aware of this association as well since they refer to Utopia as at stake here, and argue if they are wrong then “Utopia would have no need for randomness”.

But their argument is that P is not NP and so they argue a “basic goal of complexity theory is to prove that certain complexity classes e. As this is a book geared to computer science, space and time for solving problems is a problem and they take time and space to deal with both. This enters an element of practicality into what otherwise might be Platonic and Godelian. I have to wonder however that space might be more expensive than time with cmplexity price of memory these days.

One odd result of their argument in chapter 4 is that their book is not the best in its class since there ought to be still better languages to show it, but presumably those will come in time. It is easier to check a book for correctness than to write one. I would never have guessed that “the polynomial hierarchy does comptuational collapse” p. Again the difference between guessing an answer and verifying it comes up, as another version of the main difficulty.

No wonder Kirk had confidence in him on the way home. I wonder how their discussion of model comparisons would work regarding natural languages as well.

The book continues to be relevant to many other things. Never thought of it that way though they bbarak much associated traffic on the issue. In chapter 7 randomness barka the topic and the quote from Sophocles strikes me as odd – since Jocasta turns out to be wrong, the argument in the book to the contrary. Still, this is a practical book and the chapter concerns bounded-error probabilistic polynomial-time. This reminds me of an argument Stuart Kauffman makes and I was surprised not to see him in the bibliography.

A common thread through much of the book concerns various languages and it occurs to me a definition of a language would be a curious and interesting addition to the comlutational. This is especially interesting since some languages reduce to other ones.

This problem is coNP-complete, and hence is believed comlexity not have a polynomial-sized proof in the traditional sense. But I also wonder if the process does not change the class. This seems clear with socks but what about other things? Would this work in quantum mechanics for example?