ARORA BARAK COMPUTATIONAL COMPLEXITY A MODERN APPROACH PDF

Computational Complexity could have been — and still could be, in a future edition — a fine book. As it stands, however, errors seriously sabotage its potential. To accommodate a variety of audiences undergraduates, graduates, computer scientists, mathematicians, etc. The first eleven chapters lay out the basics of topics such as P and NP , randomized algorithms, interactive proofs, quantum computation, and much more. Several of the themes introduced here then reappear in more detail in Part Two five chapters on Boolean circuits, decision trees, and other models of computation and Part Three seven chapters under the heading of advanced topics. For example, Chapter 11 describes the PCP Theorem PCP stands for probabilistically checkable proof , explores it from different angles, and proves a weaker version.

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Sanjeev Arora is a Professor in the department of computer science at Princeton University. He holds a Ph. Boaz Barak is an assistant professor in the department of computer science at Princeton University.

Computational Complexity : A Modern Approach. Sanjeev Arora , Boaz Barak. 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 exercises are included with a selected hint set. The book starts with a broad introduction to the field and progresses to advanced results. Contents include: definition of Turing machines and basic time and space complexity classes, probabilistic algorithms, interactive proofs, cryptography, quantum computation, lower bounds for concrete computational models decision trees, communication complexity, constant depth, algebraic and monotone circuits, proof complexity , average-case complexity and hardness amplification, derandomization and pseudorandom constructions, and the PCP theorem.