The Golden Ticket: P, NP, and the Search for the Impossible by Lance Fortnow (PDF)

Description

The computer science problem whose solution could transform life as we know itThe P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

User’s Reviews

Editorial Reviews: From Booklist *Starred Review* In 1956, mathematician Kurt Gödel wrote to computer scientist John von Neumann speculating about how “the mental work of a mathematician . . . could be completely replaced by a machine.” In Gödel’s speculation, Fortnow finds the kernel of what may be the most important mathematical problem of all time. That as-yet-unsolved problem—identified by mathematicians as the P-NP problem—raises fundamental questions about just how far society can ride the technological wave triggered by the computer revolution. Fortnow unfolds a fascinating dual-track story of how this problem first emerged, Western researchers encountering it while trying to maximize computer efficiency, Russian analysts confronting it while puzzling over the persistent need for perebor (“brute force search”). Readers watch as the P-NP problem attracts investigators in cryptography, biology, quantum physics, and social networking—and frustrates them all. Fortnow allows nonspecialist readers to glimpse the conceptual difficulties here (try “nondeterministic polynomial time,” for example). But he mercifully frames his discussion largely in nontechnical terms. Even readers averse to mathematics will share in the intellectual stimulation of pondering a riddle compelling us to ask what we should hope for—and fear—in replacing human brains with computer algorithms. A provocative reminder of the real-world consequences of a theoretical enigma. –Bryce Christensen Review “One of Amazon.com’s 2013 Best Science Books””One of Choice’s Outstanding Academic Titles for 2013″”Honorable Mention for the 2013 PROSE Award in Popular Science & Mathematics, Association of American Publishers””As Fortnow describes. . . P versus NP is ‘one of the great open problems in all of mathematics’ not only because it is extremely difficult to solve but because it has such obvious practical applications. It is the dream of total ease, of the confidence that there is an efficient way to calculate nearly everything, ‘from cures to deadly diseases to the nature of the universe,’ even ‘an algorithmic process to recognize greatness.’. . . To postulate that P ≠ NP, as Fortnow does, is to allow for a world of mystery, difficulty, and frustration–but also of discovery and inquiry, of pleasures pleasingly delayed.”—Alexander Nazaryan, New Yorker”Fortnow effectively initiates readers into the seductive mystery and importance of P and NP problems.” ― Publishers Weekly”Fortnow’s book is just the ticket for bringing one of the major theoretical problems of our time to the level of the average citizen–and yes, that includes elected officials.”—Veit Elser, Science”Without bringing formulas or computer code into the narrative, Fortnow sketches the history of this class of questions, convincingly demonstrates their surprising equivalence, and reveals some of the most far-reaching implications that a proof of P = NP would bring about. These might include tremendous advances in biotechnology (for instance, more cures for cancer), information technology, and even the arts. Verdict: Through story and analogy, this relatively slim volume manages to provide a thorough, accessible explanation of a deep mathematical question and its myriad consequences. An engaging, informative read for a broad audience.”—J.J.S. Boyce, Library Journal”A provocative reminder of the real-world consequences of a theoretical enigma.” ― Booklist”The definition of this problem is tricky and technical, but in The Golden Ticket, Lance Fortnow cleverly sidesteps the issue with a boiled-down version. P is the collection of problems we can solve quickly, NP is the collection of problems we would like to solve. If P = NP, computers can answer all the questions we pose and our world is changed forever. It is an oversimplification, but Fortnow, a computer scientist at Georgia Institute of Technology, Atlanta, knows his stuff and aptly illustrates why NP problems are so important.”—Jacob Aron, New Scientist”Fortnow’s book does a fine job of showing why the tantalizing question is an important one, with implications far beyond just computer science.”—Rob Hardy, Commercial Dispatch”A great book. . . . [Lance Fortnow] has written precisely the book about P vs. NP that the interested layperson or IT professional wants and needs.”—Scott Aaronson, Shtetl-Optimized blog”[The Golden Ticket] is a book on a technical subject aimed at a general audience. . . . Lance’s mix of technical accuracy with evocative story telling works.”—Michael Trick, Michael Trick’s Operations Research Blog”Thoroughly researched and reviewed. Anyone from a smart high school student to a computer scientist is sure to get a lot of this book. The presentation is beautiful. There are few formulas but lots of facts.” ― Daniel Lemire’s Blog”An entertaining discussion of the P versus NP problem.”—Andrew Binstock, Dr. Dobb’s”The Golden Ticketis an extremely accessible and enjoyable treatment of the most important question of theoretical computer science, namely whether P is equal to NP.” ― Choice”The book is accessible and useful for practically anyone from smart high school students to specialists. . . . [P]erhaps the interest sparked by this book will be the ‘Golden Ticket’ for further accessible work in this area. And perhaps P=NP will start to become as famous as E=mc2.”—Michael Trick, INFORMS Journal of Computing”In any case, it is excellent to have a nontechnical book about the P versus NP question. The Golden Ticket offers an inspiring introduction for nontechnical readers to what is surely the most important open problem in computer science.”—Leslie Ann Goldberg, LMS Newsletter”The Golden Ticket does a good job of explaining a complex concept in terms that a secondary-school student will understand–a hard problem in its own right, even if not quite NP.” ― Physics World”[The Golden Ticket] is fun to read and can be fully appreciated without any knowledge in (theoretical) computer science. Fortnow’s efforts to make the difficult material accessible to non-experts should be commended.”—Andreas Maletti, Zentralblatt MATH”This is a fabulous book for both educators and students at the secondary school level and above. It does not require any particular mathematical knowledge but, rather, the ability to think. Enjoy the world of abstract ideas as you experience an intriguing journey through mathematical thinking.”—Gail Kaplan, Mathematics Teacher”Fortnow’s book provides much of the background and personal information on the main characters involved in this problem–notably Steven Cook, with a cameo appearance by Kurt Gödel–that one does not get in the more technical treatments. There is a lot of information in this book, and the serious computer science student is sure to learn from it.”—James M. Cargal, UMAP Journal”Accessible and easy to digest. . . . The Golden Ticket is a great introduction to a maths problem that few people know about and even fewer understand and a great way to try to start thinking about it and its implications.”—Johar M. Ashfaque, Mathematics Today Review “You will love this book. It’s completely accessible and captures the thrill, potential, and heartbreak of an edgy mathematical problem in terms that nonmathematicians will appreciate. After readingThe Golden Ticket, I sort of hope P isn’t NP after all.”―Vint Cerf, Internet Pioneer”The P-NP problem is fundamental to computer science, and indeed all of mathematics. This book presents an engaging exposition of the problem, its history, and importance. In the process, it touches on major topics appearing in university computer science courses, all presented in an amusing style requiring no background in mathematics beyond the ability to solve Sudoku puzzles. I highly recommend it.”―Stephen Cook, formulator of the P-NP problem”This book, written by a world-class master of the field, is a grand tour of the most celebrated and profound unsolved problem in computer science. Fortnow’s many ingenious explanations make the mysteries of computational complexity accessible to anyone interested in the fundamental questions: what can be computed and how fast can we compute it?”―John MacCormick, author of Nine Algorithms That Changed the Future”This book is meticulous. Fortnow has really tracked down the history and background of this important and timely subject. Even complexity theorists will benefit from his fine scholarship. The Golden Ticket is the first of its kind―a book for general readers about complexity theory.”―William Gasarch, University of Maryland”Nobody explains the importance of the P-NP problem better than Fortnow.”―William J. Cook, author of In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation From the Inside Flap “You will love this book. It’s completely accessible and captures the thrill, potential, and heartbreak of an edgy mathematical problem in terms that nonmathematicians will appreciate. After reading The Golden Ticket, I sort of hope P isn’t NP after all.”–Vint Cerf, Google Vice President and Chief Internet Evangelist and one of the “Fathers of the Internet””The P-NP problem is fundamental to computer science, and indeed all of mathematics. This book presents an engaging exposition of the problem, its history, and importance. In the process, it touches on major topics appearing in university computer science courses, all presented in an amusing style requiring no background in mathematics beyond the ability to solve Sudoku puzzles. I highly recommend it.”–Stephen Cook, formulator of the P-NP problem”This book, written by a world-class master of the field, is a grand tour of the most celebrated and profound unsolved problem in computer science. Fortnow’s many ingenious explanations make the mysteries of computational complexity accessible to anyone interested in the fundamental questions: what can be computed and how fast can we compute it?”–John MacCormick, author ofNine Algorithms That Changed the Future”This book is meticulous. Fortnow has really tracked down the history and background of this important and timely subject. Even complexity theorists will benefit from his fine scholarship. The Golden Ticket is the first of its kind–a book for general readers about complexity theory.”–William Gasarch, University of Maryland”Nobody explains the importance of the P-NP problem better than Fortnow.”–William J. Cook, author ofIn Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation From the Back Cover “You will love this book. It’s completely accessible and captures the thrill, potential, and heartbreak of an edgy mathematical problem in terms that nonmathematicians will appreciate. After readingThe Golden Ticket, I sort of hope P isn’t NP after all.”–Vint Cerf, Internet Pioneer”The P-NP problem is fundamental to computer science, and indeed all of mathematics. This book presents an engaging exposition of the problem, its history, and importance. In the process, it touches on major topics appearing in university computer science courses, all presented in an amusing style requiring no background in mathematics beyond the ability to solve Sudoku puzzles. I highly recommend it.”–Stephen Cook, formulator of the P-NP problem”This book, written by a world-class master of the field, is a grand tour of the most celebrated and profound unsolved problem in computer science. Fortnow’s many ingenious explanations make the mysteries of computational complexity accessible to anyone interested in the fundamental questions: what can be computed and how fast can we compute it?”–John MacCormick, author of Nine Algorithms That Changed the Future”This book is meticulous. Fortnow has really tracked down the history and background of this important and timely subject. Even complexity theorists will benefit from his fine scholarship. The Golden Ticket is the first of its kind–a book for general readers about complexity theory.”–William Gasarch, University of Maryland”Nobody explains the importance of the P-NP problem better than Fortnow.”–William J. Cook, author of In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation About the Author Lance Fortnow is professor and chair of the School of Computer Science at Georgia Institute of Technology and the founder and coauthor of the Computational Complexity blog. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A rare popular science book about the P vs NP problem. The author takes care in using concrete examples and simplifying explanations as much as possible, though I think at times he makes it too simple. I especially liked that he included the history of how the problem developed on both sides of the iron curtain during the cold war. This book may be a nice read for people who don’t have much of a science or math background, but for those who do I don’t think they will get enough out of it compared with just reading some wikipedia articles.

⭐What an awesome book! P-NP is essentially the question of whether we can find solutions quickly if we can define or know there is a solution quickly– in layman’s terms, it means we know, and then can solve, the traveling salesman problem in “P” — polynomial — rather than exponential or infinite time, or not at all. (MAHDI emailed and corrected this by saying: “The second sentence is wrong. P-NP is whether we can find solutions nearly as efficiently as we can verify them. The statement that we can find solutions if we can know there is a solution is a known fact and an easy exercise to prove”).There are a lot of technical books on the topic, but this is the first recent book that explores the golden ticket (finding the ONE in your batch of many that will allow you into Willy Wonka’s factory tour) in layman’s terms, but without talking down to the reader, and covering and focusing on all the aspects of the question. “How not to prove that P does not equal NP” as the author says, is an example of the complex and convoluted logic that’s needed to explore the field of computational complexity.Most authors, including this one, use public key crytography, factoring, etc. as examples of the “good” things about intractable problems, yet they also point out that if you could solve this problem, all the other millenium prize problems would likely also fall before you! That’s more than $5 million US, so this book is definitely worth a careful read! (Ok, little tongue in cheek). The current “go to” text on the topic, from 2010, is Goldreich’s

⭐– which takes a kind of “text” approach, with problems, exercises, etc., and is a lot more technically oriented (interpret: dry) than Fortnow.Contents include: The Golden Ticket, The Beautiful World, P and NP, The Hardest Problems in NP, The Prehistory of P vs. NP, Dealing with Hardness, Proving P does not equal NP (which this author believes), Secrets, Quantum, and The Future.This book is truly FUN and READABLE– Fortnow peppers every page with anecdotes, examples, side stories, cartoons, diagrams, and an amazing array of connections. Past explorations couldn’t even have asked if it’s possible to scan for the largest Facebook friends lists, because Facebook didn’t exist during most of the past P/NP books frames!If you want a more general intro to computational complexity, Neil Johnson’s little triple reprint from 07 to 2012 is outstanding:

⭐, and is under 10 bucks. For an exploration of how P/NP fits with the other current millenial problems, an outstanding new book is Ian Stewart’s

⭐. To go a level higher, and see how computational complexity fits more generally in Systems Science and systems thinking, Flood’s 2010 book is a gem:

⭐.NONE of these, however, are as gentle an introduction, with as complete and detailed coverage, as Fortnow. This is a must have if you have any interest in the biggest and toughest and perhaps most important problem of our age. The icing on the cake is the really fun read of a really dry topic!EMAILERS– update: For those who want more math on complexity than Fortnow gives, but not beyond advanced undergrad, check out this truly undiscovered gem by Sole:

⭐.Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it’s a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.

⭐Very interesting and powerful information.However some explanations are hazy enough that it sounds a little uncertain at times.Very particularly the author should review quantum mechanics and the “how” of so-called ‘quantum teleportation’ …. It doesn’t work as the author says, not at all.Still, extremely thought provoking in the areas the author is really conversant with.

⭐Lance Fortnow’s new book is an inspiring, accessible, and imaginative overview of P versus NP that everyone can read and appreciate, which until now has been conspicuously missing from the literature. Within the “folklore” of complexity theory, people have long uttered intuitive phrases to motivate P versus NP in passing, such as “P versus NP is asking whether creativity can be automated by computers.” Fortnow takes these intuitions and expands them, like no one else has before: really imagining a world where P = NP, exploring the magic of computing in that world, and arguing why that world is unlikely to exist. He also discusses a historical account of the problem’s origins in both the East and West, how people cope with P versus NP in practice, some past attempts at resolving P versus NP, the applications to cryptography, and the relevance of quantum computing. All this in less than 200 pages!There is an intellectual cost to the immediate accessibility of this book: for example, P and NP are never really formally defined. If you would like to *work* on P versus NP, or (less ambitiously) are looking for a technical overview of the problem, there are many available books to recommend such as Scott Aaronson’s new

⭐or Sipser’s classic textbook

⭐. However, if you’re just looking for a high-level explanation of why P versus NP is so important, Fortnow’s book is a great place to start.

⭐Having personally neglected computational theory for almost two decades since completing my doctorate in computer science, this read was a blast – not only reminding me of the main themes of the topic, but seeing a bigger perspective around it than I’d ever previously been taught – plus a lot of new aspects have developed over those years (e.g., I still thought of P/NP as being about deterministic versus non-deterministic, rather than today’s more common vantage: recognizing versus finding a solution to a problem instance).The footnote on page 111 is my favorite footnote ever.Given my background, I wouldn’t mind (for the Second Edition?) a 2- or 3-page appendix with a Wikipedia type of entry about the technical details, so I could remind myself and ruminate more deeply without interrupting my transcendental state by running back to an actual computer screen, but that is hardly a criticism of the book, given its purpose.My work is in machine learning (aka, predictive analytics), and the author touches upon how P/NP relates to my field; tantalizing food for thought. Machine learning is not just optimization, though; beyond optimizing over a training data set, you need to ensure it then continues to perform well over data not used to optimize it. Hmm, how does this play out if P=NP?Eric Siegel, Ph.D.Founder, Predictive Analytics WorldAuthor,

⭐yeah

⭐Muy decepcionante. El libro parece tratar en principio sobre el problema de P y NP, pero lo que el autor tiene que contar sobre la materia es tan poco que hay decenas de páginas de relleno. Hay partes de relleno muy divertidas e interesantes, como la completísima historia de ficción en la que se demuestra que P=NP y por tanto todo problema computacional puede reducirse a otro problema resoluble en tiempo polinómico. El autor hace en esa historia un fantástico ejercicio de imaginación comparable, creo al de alguien a quien le pidieran en 1970 qué pasaría si todo el mundo tuviera a acceso a internet.Pero luego nos llegan las disgresiones, la introducción a los algoritmos de cifrado (sin relacionarlos mucho con P=NP), la criptografía cuántica (para la que de momento no hay mucho armamento algorítmico puesto en producción)… y otras cosas que me hacen echar de menos el tema principal del libro. Un poco disperso, vaya. Lo que cuenta es interesante pero yo esperaba algo más técnico y más centrado en el tema principal.

⭐

⭐This book is definitely written for the layman, but I don’t know of any non-technical types who would be remotely interested in it.So, you can tell I was disappointed. The first thing the author does is to tell you to go elsewhere for technical background in the subject because you’re not going to find it in this book. And he’s right.The descriptions of the types of problems that fall into P and NP is mildly interesting, but the chapter about what the world would be like if P=NP is pretty much a waste of time from my point of view.I guess I should have read more about the book’s content before ordering it on-line, but I really didn’t imagine that it could be as light as it is.

⭐comprado por estar recomendado en el blog de microsiervos, está bien pero repite una y otra vez el mismo mensaje, usando multitud de ejemplos. Después de llevar más de medio libro leído resulta monótono y pierde el aliciente.

⭐

⭐I really like this book as it explains in layman terms the details of the p vs np problem and has seperate chapter on implications of p=np

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