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The P=NP Question and Gödel’s Lost Letter
? DoesP=NP. In just ?ve symbols Dick Karp –in 1972–captured one of the deepest and most important questions of all time. When he ?rst wrote his famous paper, I think it’s fair to say he did not know the depth and importance of his question. Now over three decades later, we know P=NP is central to our understanding of compu- tion, it is a very hard problem, and its resolution will have potentially tremendous consequences. This book is a collection of some of the most popular posts from my blog— Godel ̈ Lost Letter andP=NP—which I started in early 2009. The main thrust of the blog, especially when I started, was to explore various aspects of computational complexity around the famousP=NP question. As I published posts I branched out and covered additional material, sometimes a timely event, sometimes a fun idea, sometimes a new result, and sometimes an old result. I have always tried to make the posts readable by a wide audience, and I believe I have succeeded in doing this.
Introduction to Quantum Algorithms via Linear Algebra, second edition
Quantum computing explained in terms of elementary linear algebra, emphasizing computation and algorithms and requiring no background in physics. This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, it makes quantum algorithms accessible to students and researchers in computer science who have not taken courses in quantum physics or delved into fine details of quantum effects, apparatus, circuits, or theory.
DNA Based Computers III
This volume presents the proceedings from the third DIMACS workshop on "DNA Based Computers" held at the University of Pennsylvania (Philadelphia). The workshop was part of the Special Year on Molecular Biology and the Special Year on DNA Computing. The focus of this workshop was on the multidisciplinary nature of the conference, with emphasis on the interaction between biology and biochemistry on one hand and computer science and mathematics on the other.
Mechanizing Proof
Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as tradition...
The Nature of Computation
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 a...
Theory of Cryptography
This book constitutes the refereed proceedings of the Third Theory of Cryptography Conference, TCC 2006, held in March 2006. The 31 revised full papers presented were carefully reviewed and selected from 91 submissions. The papers are organized in topical sections on zero-knowledge, primitives, assumptions and models, the bounded-retrieval model, privacy, secret sharing and multi-party computation, universally-composible security, one-way functions and friends, and pseudo-random functions and encryption.
Biological Computation
The area of biologically inspired computing, or biological computation, involves the development of new, biologically based techniques for solving difficult computational problems. A unified overview of computer science ideas inspired by biology, Biological Computation presents the most fundamental and significant concepts in this area. In the book, students discover that bacteria communicate, that DNA can be used for performing computations, how evolution solves optimization problems, that the way ants organize their nests can be applied to solve clustering problems, and what the human immune system can teach us about protecting computer networks. The authors discuss more biological example...
