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Nature of Computation [Kõva köide]

(, Santa Fe Institute), (Institute of Theoretical Physics, Otto-von-Guericke University, Magdeburg, and External Professor, Santa Fe Institute)
  • Formaat: Hardback, 1008 pages, kõrgus x laius x paksus: 250x195x65 mm, kaal: 2215 g, 338 b/w line illustrations, and 30 b/w halftones
  • Ilmumisaeg: 11-Aug-2011
  • Kirjastus: Oxford University Press
  • ISBN-10: 0199233217
  • ISBN-13: 9780199233212
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  • Formaat: Hardback, 1008 pages, kõrgus x laius x paksus: 250x195x65 mm, kaal: 2215 g, 338 b/w line illustrations, and 30 b/w halftones
  • Ilmumisaeg: 11-Aug-2011
  • Kirjastus: Oxford University Press
  • ISBN-10: 0199233217
  • ISBN-13: 9780199233212
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.

Arvustused

A creative, insightful, and accessible introduction to the theory of computing, written with a keen eye toward the frontiers of the field and a vivid enthusiasm for the subject matter. * Jon Kleinberg, Cornell University * To put it bluntly: this book rocks! It's 900+ pages of awesome. It somehow manages to combine the fun of a popular book with the intellectual heft of a textbook, so much so that I don't know what to call it (but whatever the genre is, there needs to be more of it!). * Scott Aaronson, Massachusetts Institute of Technology * Moore and Mertens guide the reader through the interesting field of computational complexity in a clear, broadly accessible and informal manner, while systematically explaining the main concepts and approaches in this area and the existing links to other disciplines. The book is comprehensive and can be easily used as a textbook, at both advanced undergraduate and postgraduate levels, but is equally useful for researchers in neighbouring disciplines, such as statistical physics [ ...]. Some of the material covered, such as approximability issues and Probabilistically Checkable Proofs is typically not presented in books of this type, and the authors do an excellent job in presenting them very clearly and convincingly. * David Saad, Aston University, Birmingham * A treasure trove of ideas, concepts and information on algorithms and complexity theory. Serious material presented in the most delightful manner! * Vijay Vazirani, Georgia Instituute of Technology * In a class by itself - in The Nature of Computation, Cristopher Moore and Stephan Mertens have produced one of the most successful attempts to capture the broad scope and intellectual depth of theoretical computer science as it is practiced today. The Nature of Computation is one of those books you can open to a random page and find something amazing, surprising and, often, very funny. * American Scientist * a comprehensive, accessible, and highly enjoyable book that conveys the key intellectual contributions of the theory of computing ... a valuable resource for any educator * Haris Aziz, SIGACT * The book is highly recommended for all interested readers: in or out of courses, students undergraduate or graduate, researchers in other fields eager to learn the subject, or scholars already in the field who wish to enrich their current understanding. It makes for a great textbook in a conventional theory of computing course, as I can testify from recent personal experience (I used it once; Ill use it again!). With its broad and deep wealth of information, it would be a top contender for one of my desert island books.TNoC speaks directly, clearly, convincingly, and entetainingly, but also goes much further: it inspires. * Frederic Green, SIGACT *

Figure Credits
xiii
Preface xv
1 Prologue
1(14)
1.1 Crossing Bridges
1(4)
1.2 Intractable Itineraries
5(3)
1.3 Playing Chess With God
8(2)
1.4 What Lies Ahead
10(5)
Problems
11(2)
Notes
13(2)
2 The Basics
15(26)
2.1 Problems and Solutions
15(3)
2.2 Time, Space, and Scaling
18(5)
2.3 Intrinsic Complexity
23(2)
2.4 The Importance of Being Polynomial
25(4)
2.5 Tractability and Mathematical Insight
29(12)
Problems
30(5)
Notes
35(6)
3 Insights and Algorithms
41(54)
3.1 Recursion
42(1)
3.2 Divide and Conquer
43(10)
3.3 Dynamic Programming
53(6)
3.4 Getting There From Here
59(5)
3.5 When Greed is Good
64(4)
3.6 Finding a Better Flow
68(3)
3.7 Flows, Cuts, and Duality
71(3)
3.8 Transformations and Reductions
74(21)
Problems
76(13)
Notes
89(6)
4 Needles in a Haystack: the Class NP
95(32)
4.1 Needles and Haystacks
96(1)
4.2 A Tour of NP
97(12)
4.3 Search, Existence, and Nondeterminism
109(6)
4.4 Knots and Primes
115(12)
Problems
121(4)
Notes
125(2)
5 Who is the Hardest One of All? NP-Completeness
127(46)
5.1 When One Problem Captures Them All
128(1)
5.2 Circuits and Formulas
129(4)
5.3 Designing Reductions
133(12)
5.4 Completeness as a Surprise
145(8)
5.5 The Boundary Between Easy and Hard
153(7)
5.6 Finally, Hamiltonian Path
160(13)
Problems
163(5)
Notes
168(5)
6 The Deep Question: P vs. NP
173(50)
6.1 What if P=NP?
174(7)
6.2 Upper Bounds are Easy, Lower Bounds Are Hard
181(3)
6.3 Diagonalization and the Time Hierarchy
184(3)
6.4 Possible Worlds
187(4)
6.5 Natural Proofs
191(5)
6.6 Problems in the Gap
196(3)
6.7 Nonconstructive Proofs
199(11)
6.8 The Road Ahead
210(13)
Problems
211(7)
Notes
218(5)
7 The Grand Unified Theory of Computation
223(78)
7.1 Babbage's Vision and Hilbert's Dream
224(6)
7.2 Universality and Undecidability
230(10)
7.3 Building Blocks: Recursive Functions
240(9)
7.4 Form is Function: the λ-Calculus
249(9)
7.5 Turing's Applied Philosophy
258(6)
7.6 Computation Everywhere
264(37)
Problems
284(6)
Notes
290(11)
8 Memory, Paths, and Games
301(50)
8.1 Welcome to the State Space
302(4)
8.2 Show Me The Way
306(4)
8.3 L and NL-Completeness
310(4)
8.4 Middle-First Search and Nondeterministic Space
314(3)
8.5 You Can't Get There From Here
317(2)
8.6 PSPACE, Games, and Quantified SAT
319(9)
8.7 Games People Play
328(11)
8.8 Symmetric Space
339(12)
Problems
341(6)
Notes
347(4)
9 Optimization and Approximation
351(100)
9.1 Three Flavors of Optimization
352(3)
9.2 Approximations
355(9)
9.3 Inapproximability
364(6)
9.4 Jewels and Facets: Linear Programming
370(12)
9.5 Through the Looking-Glass: Duality
382(5)
9.6 Solving by Balloon: Interior Point Methods
387(5)
9.7 Hunting with Eggshells
392(10)
9.8 Algorithmic Cubism
402(7)
9.9 Trees, Tours, and Polytopes
409(5)
9.10 Solving Hard Problems in Practice
414(37)
Problems
427(15)
Notes
442(9)
10 Randomized Algorithms
451(56)
10.1 Foiling the Adversary
452(2)
10.2 The Smallest Cut
454(3)
10.3 The Satisfied Drunkard: WalkSAT
457(3)
10.4 Solving in Heaven, Projecting to Earth
460(5)
10.5 Games Against the Adversary
465(7)
10.6 Fingerprints, Hash Functions, and Uniqueness
472(7)
10.7 The Roots of Identity
479(3)
10.8 Primality
482(6)
10.9 Randomized Complexity Classes
488(19)
Problems
491(11)
Notes
502(5)
11 Interaction and Pseudorandomness
507(56)
11.1 The Tale of Arthur and Merlin
508(13)
11.2 The Fable of the Chess Master
521(5)
11.3 Probabilistically Checkable Proofs
526(14)
11.4 Pseudorandom Generators and Derandomization
540(23)
Problems
553(7)
Notes
560(3)
12 Random Walks and Rapid Mixing
563(88)
12.1 A Random Walk in Physics
564(4)
12.2 The Approach to Equilibrium
568(5)
12.3 Equilibrium Indicators
573(3)
12.4 Coupling
576(3)
12.5 Coloring a Graph, Randomly
579(7)
12.6 Burying Ancient History: Coupling from the Past
586(16)
12.7 The Spectral Gap
602(4)
12.8 Flows of Probability: Conductance
606(6)
12.9 Expanders
612(11)
12.10 Mixing in Time and Space
623(28)
Problems
626(17)
Notes
643(8)
13 Counting, Sampling, and Statistical Physics
651(72)
13.1 Spanning Trees and the Determinant
653(5)
13.2 Perfect Matchings and the Permanent
658(4)
13.3 The Complexity of Counting
662(6)
13.4 From Counting to Sampling, and Back
668(6)
13.5 Random Matchings and Approximating the Permanent
674(9)
13.6 Planar Graphs and Asymptotics on Lattices
683(10)
13.7 Solving the Ising Model
693(30)
Problems
703(15)
Notes
718(5)
14 When Formulas Freeze: Phase Transitions in Computation
723(96)
14.1 Experiments and Conjectures
724(6)
14.2 Random Graphs, Giant Components, and Cores
730(12)
14.3 Equations of Motion: Algorithmic Lower Bounds
742(6)
14.4 Magic Moments
748(11)
14.5 The Easiest Hard Problem
759(9)
14.6 Message Passing
768(15)
14.7 Survey Propagation and the Geometry of Solutions
783(10)
14.8 Frozen Variables and Hardness
793(26)
Problems
796(14)
Notes
810(9)
15 Quantum Computation
819(92)
15.1 Particles, Waves, and Amplitudes
820(3)
15.2 States and Operators
823(10)
15.3 Spooky Action at a Distance
833(8)
15.4 Algorithmic Interference
841(7)
15.5 Cryptography and Shor's Algorithm
848(14)
15.6 Graph Isomorphism and the Hidden Subgroup Problem
862(7)
15.7 Quantum Haystacks: Grover's Algorithm
869(7)
15.8 Quantum Walks and Scattering
876(35)
Problems
888(14)
Notes
902(9)
A Mathematical Tools
911(34)
A.1 The Story of O
911(3)
A.2 Approximations and Inequalities
914(3)
A.3 Chance and Necessity
917(6)
A.4 Dice and Drunkards
923(4)
A.5 Concentration Inequalities
927(4)
A.6 Asymptotic Integrals
931(2)
A.7 Groups, Rings, and Fields
933(12)
Problems
939(6)
References 945(29)
Index 974
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.