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Computer science and physics have been closely linked since the
birth of modern computing. In recent years, an interdisciplinary
area has blossomed at the junction of these fields, connecting
insights from statistical physics with basic computational
challenges. Researchers have successfully applied techniques from
the study of phase transitions to analyze NP-complete problems such
as satisfiability and graph coloring. This is leading to a new
understanding of the structure of these problems, and of how
algorithms perform on them.
Computer science and physics have been closely linked since the
birth of modern computing. In recent years, an interdisciplinary
area has blossomed at the junction of these fields, connecting
insights from statistical physics with basic computational
challenges. Researchers have successfully applied techniques from
the study of phase transitions to analyze NP-complete problems such
as satisfiability and graph coloring. This is leading to a new
understanding of the structure of these problems, and of how
algorithms perform on them.
In the last decade, the boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. Every passing year shows that physicists and computer scientists have a great deal to say to each other, sharing metaphors, intuitions, and mathematical techniques. In this book, two leading researchers in this area introduce the reader to the fundamental concepts of computational complexity. They go beyond the usual discussion of P, NP and NP-completeness to explain the deep meaning of the P vs. NP question, and explain many recent results which have not yet appeared in any textbook. They then give in-depth explorations of the major interfaces between computer science and physics: phase transitions in NP-complete problems, Monte Carlo algorithms, and quantum computing. The entire book is written in an informal style that gives depth with a minimum of mathematical formalism, exposing the heart of the matter without belabouring technical details. The only mathematical prerequisites are linear algebra, complex numbers, and Fourier analysis (and most chapters can be understood without even these). It can be used as a textbook for graduate students or advanced undergraduates, and will be enjoyed by anyone who is interested in understanding the rapidly changing field of theoretical computer science and its relationship with other sciences.
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