The P=NP Question and Gödel’s Lost Letter

ISBN-13: 9781489992727 / Angielski / Miękka / 2014 / 239 str.

Richard J. Lipton

Opis

? 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.

Recenzje

"This book is a thoroughly enjoyable read because of the great balance between anecdotes, presentations of 'nice' problems and algorithms and their solutions and proofs, 'hard mathematics,' and musings on how to approach mathematical problems. After having read the book, most readers with a background in complexity theory will most likely be unable to resist immediately working on at least one of the many open problems presented in the book." (Till Tantau, Mathematical Reviews, October, 2015)

"This book ... collects and edits the highlights from Lipton's ongoing blog, rounded out by cross-references and a useful index and bibliography. ... the book offers a different experience and a framed portrait of the state of the art. ... Summing Up: Recommended. All levels/libraries." (D. V. Feldman, Choice, Vol. 48 (9), May, 2011)

"The P=NP question is certainly one of the most important problems in mathematics and computer science (CS). What makes this book unique and delightful is that it gives proper weight to the question rather than the technicalities. Each chapter is based on one of Lipton's blog posts, and readers can jump from chapter to chapter to find his beautifully written thoughts and insights. ... In fact, anyone who is highly motivated by this interesting subject that relates science with reality should read it." (Hector Zenil, ACM Computing Reviews, March, 2011)

"This book collects some entries of the author's blog on Gödel's lost letter and P = NP ... . It is an enjoyable and lively introduction to some impressive achievements in the field of complexity theory." (Thierry Coquand, Zentralblatt MATH, Vol. 1215, 2011)

Spis treści

The Problem.- G¨odel’s Lost Letter.- Cook’s Insight.- Karp Hits Twenty-One.- Nondeterminism.- Why Polynomial Time?.- P=NP and Insider Baseball.- The Knapsack Problem: An Exponential Algorithm.- A Nightmare about P=NP.- The One Page Challenge.- P=NP and Big O Notation.- More Abuse of O-Notation.- Our Problem is More Important Than Your Problem.- The Magic of P 6= NP.- P=NP and the End of Security.- The LBA Problem.- P=NP and The Three Bears.- Bait and Switch: Why Lower Bounds Are So Hard.- The Knapsack Problem: A Lower Bound.- There are Big Circuits Out There.- Knapsack: An Upper Bound.- Hilbert and P=NP.- Are All NP-Complete Problems The Same?.- The Real P=NP Problem.- P=NP in Other Worlds.- P=NP and the Structure of the World.- Do Impossibility Results Matter?.- Circuit Lower Bounds.- The Core of a Problem Who is Afraid of Natural Proofs?.- False Proofs by Famous People.- Cryptography Turned Upside Down Ramsey’s Theorem Meets P=NP.- Shooting Down Proofs P=NP.- Where are the Movies?.- P=NP : What are the Odds?.-

O autorze

Richard Lipton is the Storey Professor of Computer Science at Georgia Institute of Technology. Previously he held faculty positions at Yale University, the University of California at Berkeley, and Princeton University. His research is focused primarily, but not exclusively, on theory of computation. He has made seminal contributions to many areas of computing from software engineering and program testing, to computer security and cryptography, to DNA and molecular computation, and to other areas of computer science. He is a member of The National Academy of Engineering, an ACM Fellow, and a Guggenheim fellow.

Blurb

The P=NP question is one of the great problems of science, which has intrigued computer scientists and mathematicians for decades. Despite the abundant research in theoretical computer science regarding the P=NP question, it has not been solved.

The P=NP Question and Gödel’s Lost Letter covers historical developments (including the Gödel’s Lost letter), the importance of P=NP and the future of P=NP. This guide is also based on a new blog by the author, located at http://rjlipton.wordpress.com. Jin-Yi Cai, a professor in computer science at the University of Wisconsin remarks 'I think it is the single most interesting web blog I have seen on related topics. He has a great insight and wit and beautiful way to see things and explain them.' Richard DeMillo, a professor in computer science at Georgia Tech remarks, 'This is a much needed treatment of great open problem computing.'

The P=NP Question and Gödel’s Lost Letter is designed for advanced level students and researchers in computer science, and mathematics as a secondary text and reference book. Computer programmers, software developers and IT professionals working in the related industry of computer science theory, will also find this guide a valuable asset.