The nature of computation:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2017
|
| Edition: | Reprinted 2017 (with corrections) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 985 Seiten Illustrationen, Diagramme |
| ISBN: | 9780199233212 |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Figure Credits xiii
Preface xv
1 Prologue 1
1.1 Crossing Bridges................................................................... 1
1.2 Intractable Itineraries ........................................................... 5
1.3 Playing Chess With God............................................................. 8
1.4 What Lies Ahead................................................................... 10
Problems............................................................................... 11
Notes ................................................................................. 13
2 The Basics 15
2.1 Problems and Solutions............................................................ 15
2.2 Time, Space, and Scaling.......................................................... 18
2.3 Intrinsic Complexity.............................................................. 23
2.4 The Importance of Being Polynomial................................................ 25
2.5 Tractability and Mathematical Insight............................................. 29
Problems............................................................................... 30
Notes ................................................................................. 35
3 Insights and Algorithms 41
3.1 Recursion......................................................................... 42
3.2 Divide and Conquer................................................................ 43
3.3 Dynamic Programming............................................................... 53
3.4 Getting There From Here........................................................... 59
3.5 When Greed is Good................................................................ 64
3.6 Finding a Better Flow............................................................. 68
3.7 Flows, Cuts, and Duality.......................................................... 71
3.8 Transformations and Reductions.................................................... 74
Problems............................................................................... 76
Notes ................................................................................. 89
4 Needles in a Haystack: the Class NP 95
4.1 Needles and Haystacks........................................................... 96
4.2 A Tour of NP.................................................................... 97
4.3 Search, Existence, and Nondeterminism.......................................... 109
4.4 Knots and Primes .............................................................. 115
Problems............................................................................ 121
Notes .............................................................................. 125
5 Who is the Hardest One of All? NP-Completeness 127
5.1 When One Problem Captures Them All............................................. 128
5.2 Circuits and Formulas......................................................... 129
5.3 Designing Reductions........................................................... 133
5.4 Completeness as a Surprise..................................................... 145
5.5 The Boundary Between Easy and Hard............................................. 153
5.6 Finally, Hamiltonian Path...................................................... 160
Problems............................................................................ 163
Notes .............................................................................. 168
6 The Deep Question: P vs. NP 173
6.1 What ifP=NP? .................................................................. 174
6.2 Upper Bounds are Easy, Lower Bounds Are Hard................................... 181
6.3 Diagonalization and the Time Hierarchy......................................... 184
6.4 Possible Worlds................................................................ 187
6.5 Natural Proofs................................................................. 191
6.6 Problems in the Gap ........................................................... 196
6.7 Nonconstructive Proofs......................................................... 199
6.8 The Road Ahead ................................................................ 210
Problems........................................................................... 2If
Notes .............................................................................. 218
7 The Grand Unified Theory of Computation 223
7.1 Babbage’s Vision and Hilbert’s Dream........................................... 224
7.2 Universality and Undecidability................................................ 230
7.3 Building Blocks: Recursive Functions........................................... 240
7.4 Form is Function: the A-Calculus............................................... 249
7.5 Turing’s Applied Philosophy.................................................... 258
7.6 Computation Everywhere ........................................................ 264
Problems............................................................................ 284
Notes .............................................................................. 290
8 Memory, Paths, and Games 301
8.1 Welcome to the State Space..................................................... 302
8.2 Show Me The Way................................................................ 306
8.3 L and NL-Completeness.......................................................... 310
8.4 Middle-First Search and Nondeterministic Space................................... 314
8.5 You Can’t Get There From Here.................................................... 317
8.6 PSPACE, Games, and Quantified SAT ............................................... 319
8.7 Games People Play................................................................ 328
8.8 Symmetric Space.................................................................. 339
Problems.............................................................................. 341
Notes ................................................................................ 347
9 Optimization and Approximation 351
9.1 Three Flavors of Optimization.................................................... 352
9.2 Approximations................................................................... 355
9.3 Inapproximability................................................................ 364
9.4 Jewels and Facets: Linear Programming............................................ 370
9.5 Through the Looking-Glass: Duality............................................... 382
9.6 Solving by Balloon: Interior Point Methods....................................... 387
9.7 Hunting with Eggshells .......................................................... 392
9.8 Algorithmic Cubism............................................................... 402
9.9 Trees, Tours, and Polytopes ..................................................... 409
9.10 Solving Hard Problems in Practice................................................ 414
Problems.............................................................................. 427
Notes ................................................................................ 442
10 Randomized Algorithms 451
10.1 Foiling the Adversary............................................................ 452
10.2 The Smallest Cut................................................................. 454
10.3 The Satisfied Drunkard: WalkSAT.................................................. 457
10.4 Solving in Heaven, Projecting to Earth .......................................... 460
10.5 Games Against the Adversary...................................................... 465
10.6 Fingerprints, Hash Functions, and Uniqueness..................................... 472
10.7 The Roots of Identity............................................................ 479
10.8 Primality........................................................................ 482
10.9 Randomized Complexity Classes.................................................... 488
Problems.............................................................................. 491
Notes ................................................................................ 502
11 Interaction and Pseudorandomness 507
11.1 The Tale of Arthur and Merlin.................................................... 508
11.2 The Fable of the Chess Master.................................................... 521
11.3 Probabilistically Checkable Proofs............................................... 526
11.4 Pseudorandom Generators and Derandomization...................................... 540
Problems.............................................................................. 553
Notes ................................................................................ 560
12 Random Walks and Rapid Mixing 563
12.1 A Random Walk in Physics......................................................... 564
12.2 The Approach to Equilibrium...................................................... 568
12.3 Equilibrium Indicators........................................................... 573
12.4 Coupling......................................................................... 576
12.5 Coloring a Graph, Randomly....................................................... 579
12.6 Burying Ancient History: Coupling from the Past.................................. 586
12.7 The Spectral Gap................................................................. 602
12.8 Flows of Probability: Conductance................................................ 606
12.9 Expanders........................................................................ 612
12.10 Mixing in Time and Space........................................................ 623
Problems.............................................................................. 626
Notes ................................................................................ 643
13 Counting, Sampling, and Statistical Physics 651
13.1 Spanning Trees and the Determinant............................................... 653
13.2 Perfect Matchings and the Permanent ............................................. 658
13.3 The Complexity of Counting....................................................... 662
13.4 From Counting to Sampling, and Back.............................................. 668
13.5 Random Matchings and Approximating the Permanent................................. 674
13.6 Planar Graphs and Asymptotics on Lattices........................................ 683
13.7 Solving the Ising Model.......................................................... 693
Problems.............................................................................. 703
Notes ................................................................................ 718
14 When Formulas Freeze: Phase Transitions in Computation 723
14.1 Experiments and Conjectures...................................................... 724
14.2 Random Graphs, Giant Components, and Cores....................................... 730
14.3 Equations of Motion: Algorithmic Lower Bounds ................................... 742
14.4 Magic Moments.................................................................... 748
14.5 The Easiest Hard Problem......................................................... 759
14.6 Message Passing.................................................................. 768
14.7 Survey Propagation and the Geometry of Solutions................................. 783
14.8 Frozen Variables and Hardness.................................................... 793
Problems.............................................................................. 796
Notes ................................................................................ 810
15 Quantum Computation 819
15.1 Particles, Waves, and Amplitudes................................................. 820
15.2 States and Operators............................................................. 823
15.3 Spooky Action at a Distance...................................................... 833
15.4 Algorithmic Interference......................................................... 841
15.5 Cryptography and Shor’s Algorithm................................................ 848
15.6 Graph Isomorphism and the Hidden Subgroup Problem................................ 862
15.7 Quantum Haystacks: Grover’s Algorithm........................................... 869
15.8 Quantum Walks and Scattering ................................................... 876
Problems............................................................................. 888
Notes ............................................................................... 902
A Mathematical Tools 911
A.1 The Story of 0.................................................................. 911
A.2 Approximations and Inequalities................................................. 914
A.3 Chance and Necessity............................................................ 917
A.4 Dice and Drunkards.............................................................. 923
A.5 Concentration Inequalities...................................................... 927
A.6 Asymptotic Integrals............................................................ 931
A.7 Groups, Rings, and Fields....................................................... 933
Problems............................................................................. 939
References 945
Index 974
|
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | Reprinted 2017 (with corrections) |
| format | Book |
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| spelling | Moore, Cristopher 1968- Verfasser (DE-588)1014982626 aut The nature of computation Cristopher Moore ; Stephan Mertens Reprinted 2017 (with corrections) Oxford Oxford University Press 2017 xvii, 985 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Berechnungskomplexität (DE-588)4134751-1 s Komplexitätstheorie (DE-588)4120591-1 s DE-604 Mertens, Stephan Verfasser (DE-588)13040134X aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029839529&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Moore, Cristopher 1968- Mertens, Stephan The nature of computation Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4120591-1 (DE-588)4134751-1 (DE-588)4123623-3 |
| title | The nature of computation |
| title_auth | The nature of computation |
| title_exact_search | The nature of computation |
| title_full | The nature of computation Cristopher Moore ; Stephan Mertens |
| title_fullStr | The nature of computation Cristopher Moore ; Stephan Mertens |
| title_full_unstemmed | The nature of computation Cristopher Moore ; Stephan Mertens |
| title_short | The nature of computation |
| title_sort | the nature of computation |
| topic | Computational complexity Komplexitätstheorie (DE-588)4120591-1 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Computational complexity Komplexitätstheorie Berechnungskomplexität Lehrbuch |
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