計算的本質 (英文) 克里 斯托弗.摩爾 斯蒂芬.默滕斯 9787523206591 【台灣高等教育出版社】

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書名:計算的本質 (英文)
ISBN:9787523206591
出版社:世界圖書出版有限公司
著編譯者:克里 斯托弗.摩爾 斯蒂芬.默滕斯
頁數:985
所在地:中國大陸 *此為代購商品
書號:1583352
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內容簡介

計算複雜性是現代數學中最美的領域之一,它與從物理學到生物學的其他科學也息息相關。但這種美往往被不必要的形式主義所掩蓋,而互動式證明、密碼學和量子計算等令人興奮的最新成果常常被認為過於「先進」,無法向普通學生展現。這本書的目的是通過以一種清晰而愉悅的方式解釋理論計算機科學的深刻思想來予以彌合。書中包括很多有趣且深刻的主題:Pvs。NP問題;迷宮和棋牌遊戲的複雜性;優化和估計;隨機化演算法、互動式證明和偽隨機性;馬爾可夫鏈和相變;以及量子計算等。

目錄

Figure Credits
Preface
1 Prologue
1 1 CrossingBridges
1 2 IntractableItineraries
1 3 Playing ChessWith God
1 4 What LiesAhead
Problems
Notes
2 The Basics
2 1 Problems and Solutions
2 2 Time,Space,and Scaling
2 3 Intrinsic Complexity
2 4 The Importance ofBeingPolynomial
2 5 TractabilityandMathematicalInsight
Problems
Notes
3 Insights and Algorithms
3 1 Recursion
3 2 Divide and Conquer
3 3 DynamicProgramming
3 4 GettingThere FromHere
3 5 When Greedis Good
3 6 FindingaBetterFlow
3 7 Flows,Cuts,and Duality
3 8 Transformations andReductions
Problems
Notes
4 NeedlesInaHaystack:theClassNP
4 1 Needles andHaystacks
4 2 AT0ur 0fNP
4 3 Search。Existence,andNondeterminism
4 4 Knots and Primes
Problems
Notes
5 WhO is the Hardest One of All?NP-Completeness
5 1 Ⅵmen 0ne Problem CapturesThemAll
5 2 Circuits andFormulas
5 3 DesigningReductions
5 4 Completeness as aSurprise
5 5 The BoundaryBetween EasyandHard
5 6 Finally,Hamfltonian path
Problems
Notes
6 The Deep Question:P vs NP
6 1 WhatifP=NP
6 2 UpperBounds are Easy,LowerBoundsAre Hard
6 3 Diagonalization andthe Time Hierarchy
6 4 PossibleWbrlds
6 5 NaturalProofs
6 6 Problemsinthe Gap
6 7 Nonconstructive PrOOfs
6 8 The RoadAhead
Problems
Notes
7 The Grand Unified Theory of Computation
7 1 Babbage~Vision and Hilbert's Dream
7 2 Universalityand Undecidabnit、
7 3 BuildingBlocks:Recursive Functions
7 4 Formis Function:the A—Calculus
7 5 Turing'sApplied Philosophy
7 6 ComputationEverywhere
Problems
Notes
8 Memory,Paths,and Games
8 1 Wlelcometothe State Space
8 2 ShowMe TheWay
8 3 LandNL Completeness
8 4 Middle First Search and Nondeterministic Space
8 5 Y0u Cant GetThereFromHere
8 6 PSPACE,Games,and Quantified SAT
8 7 Games People Play
8 8 Symmetric Space
Problems
Notes
9 Optimization and Approximation
9 1 Three Flavors ofOptimization
9 2 Approximations
9 3 Inapproximability
9 4 Jewels andFacets:LinearProgramming
9 5 Throughthe Looking-Glass:Duality
9 6 SolvingbyBalloon:InteriorPointMethods
9 7 Huntingwitll EggsheHs
9 8 A1gorithmic Cubism
9 9 Trees,Tours,andPolytopes
9 10 SolvingHard ProblemsinPractice
Problems
Notes
10 Randomized Algorithms
10 1 FoilingtheAdversary
10 2 111e SmallestCut
10 3 The Satisfied Drunkard:WalkSAT
10 4 Solvingin Heaven Projectingto Earth
10 5 GamesAgainsttheAdversary
10 6 Fingerprints,HashFunctions,andUniqueness
10 7 The Roots ofIdentity
10 8 Primalit、
10 9 Randomized ComplexityClasses
Problems
Notes
11 Interacflon and Pseudorandomness
11 1 TheTale ofArthurandMerlin
11 2 The Fable ofthe Chess Master
11 3 ProbabilisticallyCheckable Proofs
11 4 Pseudorandom Generators and Derandomization
Problems
Nores
12 Random Walks and Rapid Mixing
12 1 A Random、^mkin Physics
12 2 The Approachto Equfl~rium
12 3 EquflibriumIndicators
12 4 Coupling

12 5 Coloring aGraph Randomly
12 6 BuryingAncientHistory:CouplingfromthePast
12 7 The Spectral Gap
12 8 FlOWS ofProbabnity:Conductance
12 9 Expanders
12 10 MixinginTime andSpace
Problems
Notes
13 Counting,Sampling,and StatisflcM Physics
13 1 SpanningTrees andthe Determinant
13 2 PerfectMatchings andthe Permanent
13 3 The ComplexityofCounting
13 4 From Countingto Sampling and Back
13 5 RandomMatchings andApproximatingthePermanent
13 6 P1anal:Graphs andAsymptotics onLattices
13 7 SolvingtheIsingModel
Problems
Notes
14 When Formulas Freeze:Phase Transitons in Computation
14 1 Experiments and Coniectures
14 2 Random Graphs,Giant Components,and Cores
14 3 Equations of Motion:Algorithmic Lower Bounds
14 4 Magic Moments
14 5 The Easiest Hard
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