The Nature of Computation

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OUP Oxford, Aug 11, 2011 - Science - 1004 pages
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Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

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Figure Credits
The Basics
Insights and Algorithms
the ClassNP
Who is the HardestOne ofAll? NPCompleteness
P vs
Optimization andApproximation 9 1 Three Flavors of Optimization 9 2 Approximations
Random Walks andRapidMixing 12 1 A Random Walk inPhysics 12 2 The Approach
Counting Sampling andStatistical Physics 13 1 Spanning Trees
PhaseTransitions inComputation 14 1 Experiments and Conjectures 14 2 Random GraphsGiant Components and Cores
Quantum Computation
A Mathematical Tools A 1 The Storyof O A 2 Approximations and Inequalities A 3 Chance and Necessity A 4 Dice and Drunkards A 5 Concentratio...

Randomized Algorithms

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About the author (2011)

Cristopher Moore graduated from Northwestern University with honors in 1986, at the age of 18, with a B.A. in Mathematics, Physics, and Integrated Science. He received his Ph.D. in Physics from Cornell University at the age of 23. After a postdoc at the Santa Fe Institute, he joined the faculty of the University of New Mexico, where he holds joint appointments in Computer Science and Physics and Astronomy. He has written over 90 papers, on topics ranging from undecidability in dynamical systems, to quantum computing, to phase transitions in NP-complete problems, to the analysis of social and biological networks. Stephan Mertens got his Diploma in Physics in 1989, and his Ph.D. in Physics in 1991, both from Georg-August University Göttingen. He holds scholarships from the "Studienstiftung des Deutschen Volkes", Germany's most prestigious organisation sponsoring the academically gifted. After his Ph.D. he worked for three years in the software industry before he joined the faculty of Otto-von-Guericke University Magdeburg as a theoretical physicist. His research focuses on disordered systems in statistical mechanics, average case complexity of algorithms, and parallel computing.