计算复杂性

计算复杂性
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作者: [以色列]
出版社: 人民邮电出版社
2010-04
版次: 1
ISBN: 9787115224002
定价: 99.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 603页
字数: 754千字
正文语种: 英语
原版书名: Computational Complexity: A Conceptual Perspective
  •   复杂性理论是计算机科学的理论基础的核心。本书是著名计算机科学家OdedGoldreich的力作,书中对计算任务固有复杂性研究进行了概念性介绍,全面分析了复杂性理论的现代主题。
      本书涉及复杂性理论的很多子领域(如难度放大、伪随机性及概率证明系统等),涵盖了NP完整性、空间复杂性、随机性和计数、伪随机数生成器等内容,还在附录里面介绍了现代密码学基础等。
      本书内容严谨,可读性强,适合作为高年级本科生、研究生的教材。同时,书中展示了复杂性理论的很多子领域,也适合领域专家参考。   OdedGoldreich,以色列魏茨曼科学研究院(WeizmannInstituteofScience)计算机科学教授,MeyerW.Weisgal讲席教授。他是SIAMJournalonComputing、JournalofCryptology和ComputationalComplexity杂志的特约编辑。其主要研究方向是计算复杂性、随机性与计算以及密码学,他在这几个方面均有享誉世界的研究成果。作为一名活跃的学者,他发表了大量的论文,还著有两卷本的FoundationsofCryptography(《密码学基础》)和ModernCryptography,ProbabilisticProofsandPseudorandomness等专著。 1IntroductionandPreliminaries1
    1.1Introduction1
    1.1.1ABriefOverviewofComplexityTheory2
    1.1.2CharacteristicsofComplexityTheory6
    1.1.3ContentsofThisBook8
    1.1.4ApproachandStyleofThisBook12
    1.1.5StandardNotationsandOtherConventions16
    1.2ComputationalTasksandModels17
    1.2.1Representation18
    1.2.2ComputationalTasks18
    1.2.3UniformModels(Algorithms)20
    1.2.4Non-uniformModels(CircuitsandAdvice)36
    1.2.5ComplexityClasses42
    ChapterNotes43

    2P,NP,andNP-Completeness44
    2.1ThePVersusNPQuestion46
    2.1.1TheSearchVersion:FindingVersusChecking47
    2.1.2TheDecisionVersion:ProvingVersusVerifying50
    2.1.3EquivalenceoftheTwoFormulations54
    2.1.4TwoTechnicalCommentsRegardingNP55
    2.1.5TheTraditionalDefinitionofNP55
    2.1.6InSupportofPDifferentfromNP57
    2.1.7PhilosophicalMeditations58
    2.2Polynomial-TimeReductions58
    2.2.1TheGeneralNotionofaReduction59
    2.2.2ReducingOptimizationProblemstoSearchProblems61
    2.2.3Self-ReducibilityofSearchProblems63
    2.2.4DigestandGeneralPerspective67
    2.3NP-Completeness67
    2.3.1Definitions68
    2.3.2TheExistenceofNP-CompleteProblems69
    2.3.3SomeNaturalNP-CompleteProblems71
    2.3.4NPSetsThatAreNeitherinPnorNP-Complete81
    2.3.5ReflectionsonCompleteProblems85
    2.4ThreeRelativelyAdvancedTopics87
    2.4.1PromiseProblems87
    2.4.2OptimalSearchAlgorithmsforNP92
    2.4.3TheClasscoNPandItsIntersectionwithNP94
    ChapterNotes97
    Exercises99

    3VariationsonPandNP108
    3.1Non-uniformPolynomialTime(P/poly)108
    3.1.1BooleanCircuits109
    3.1.2MachinesThatTakeAdvice111
    3.2ThePolynomial-TimeHierarchy(PH)113
    3.2.1AlternationofQuantifiers114
    3.2.2Non-deterministicOracleMachines117
    3.2.3TheP/polyVersusNPQuestionandPH119
    ChapterNotes121
    Exercises122

    4MoreResources,MorePower127
    4.1Non-uniformComplexityHierarchies128
    4.2TimeHierarchiesandGaps129
    4.2.1TimeHierarchies129
    4.2.2TimeGapsandSpeedup136
    4.3SpaceHierarchiesandGaps139
    ChapterNotes139
    Exercises140

    5SpaceComplexity143
    5.1GeneralPreliminariesandIssues144
    5.1.1ImportantConventions144
    5.1.2OntheMinimalAmountofUsefulComputationSpace145
    5.1.3TimeVersusSpace146
    5.1.4CircuitEvaluation153
    5.2LogarithmicSpace153
    5.2.1TheClassL154
    5.2.2Log-SpaceReductions154
    5.2.3Log-SpaceUniformityandStrongerNotions155
    5.2.4UndirectedConnectivity155
    5.3Non-deterministicSpaceComplexity162
    5.3.1TwoModels162
    5.3.2NLandDirectedConnectivity164
    5.3.3ARetrospectiveDiscussion171
    5.4PSPACEandGames172
    ChapterNotes175
    Exercises175

    6RandomnessandCounting184
    6.1ProbabilisticPolynomialTime185
    6.1.1BasicModelingIssues186
    6.1.2Two-SidedError:TheComplexityClassBPP189
    6.1.3One-SidedError:TheComplexityClassesRPandcoRP193
    6.1.4Zero-SidedError:TheComplexityClassZPP199
    6.1.5RandomizedLog-Space199
    6.2Counting202
    6.2.1ExactCounting202
    6.2.2ApproximateCounting211
    6.2.3SearchingforUniqueSolutions217
    6.2.4UniformGenerationofSolutions220
    ChapterNotes227
    Exercises230

    7TheBrightSideofHardness241
    7.1One-WayFunctions242
    7.1.1GeneratingHardInstancesandOne-WayFunctions243
    7.1.2AmplificationofWeakOne-WayFunctions245
    7.1.3Hard-CorePredicates250
    7.1.4ReflectionsonHardnessAmplification255
    7.2HardProblemsinE255
    7.2.1AmplificationwithRespecttoPolynomial-SizeCircuits257
    7.2.2AmplificationwithRespecttoExponential-SizeCircuits270
    ChapterNotes277
    Exercises278

    8PseudorandomGenerators284
    Introduction285
    8.1TheGeneralParadigm288
    8.2General-PurposePseudorandomGenerators290
    8.2.1TheBasicDefinition291
    8.2.2TheArchetypicalApplication292
    8.2.3ComputationalIndistinguishability295
    8.2.4AmplifyingtheStretchFunction299
    8.2.5Constructions301
    8.2.6Non-uniformlyStrongPseudorandomGenerators304
    8.2.7StrongerNotionsandConceptualReflections305
    8.3DerandomizationofTime-ComplexityClasses307
    8.3.1DefiningCanonicalDerandomizers308
    8.3.2ConstructingCanonicalDerandomizers310
    8.3.3TechnicalVariationsandConceptualReflections313
    8.4Space-BoundedDistinguishers315
    8.4.1DefinitionalIssues316
    8.4.2TwoConstructions318
    8.5Special-PurposeGenerators325
    8.5.1PairwiseIndependenceGenerators326
    8.5.2Small-BiasGenerators329
    8.5.3RandomWalksonExpanders332
    ChapterNotes334
    Exercises337

    9ProbabilisticProofSystems349
    9.1InteractiveProofSystems352
    9.1.1MotivationandPerspective352
    9.1.2Definition354
    9.1.3ThePowerofInteractiveProofs357
    9.1.4VariantsandFinerStructure:AnOverview363
    9.1.5OnComputationallyBoundedProvers:AnOverview366
    9.2Zero-KnowledgeProofSystems368
    9.2.1DefinitionalIssues369
    9.2.2ThePowerofZero-Knowledge372
    9.2.3ProofsofKnowledge-AParentheticalSubsection378
    9.3ProbabilisticallyCheckableProofSystems380
    9.3.1Definition381
    9.3.2ThePowerofProbabilisticallyCheckableProofs383
    9.3.3PCPandApproximation398
    9.3.4MoreonPCPItself:AnOverview401
    ChapterNotes404
    Exercises406

    10RelaxingtheRequirements416
    10.1Approximation417
    10.1.1SearchorOptimization418
    10.1.2DecisionorPropertyTesting423
    10.2Average-CaseComplexity428
    10.2.1TheBasicTheory430
    10.2.2Ramifications442
    ChapterNotes451
    Exercises453

    Epilogue461
    AppendixA:GlossaryofComplexityClasses463
    A.1Preliminaries463
    A.2Algorithm-BasedClasses464
    A.2.1TimeComplexityClasses464
    A.2.2SpaceComplexityClasses467
    A.3Circuit-BasedClasses467

    AppendixB:OntheQuestforLowerBounds469
    B.1Preliminaries469
    B.2BooleanCircuitComplexity471
    B.2.1BasicResultsandQuestions472
    B.2.2MonotoneCircuits473
    B.2.3Bounded-DepthCircuits473
    B.2.4FormulaSize474
    B.3ArithmeticCircuits475
    B.3.1UnivariatePolynomials476
    B.3.2MultivariatePolynomials476
    B.4ProofComplexity478
    B.4.1LogicalProofSystems480
    B.4.2AlgebraicProofSystems480
    B.4.3GeometricProofSystems481

    AppendixC:OntheFoundationsofModernCryptography482
    C.1IntroductionandPreliminaries482
    C.1.1TheUnderlyingPrinciples483
    C.1.2TheComputationalModel485
    C.1.3OrganizationandBeyond486
    C.2ComputationalDifficulty487
    C.2.1One-WayFunctions487
    C.2.2Hard-CorePredicates489
    C.3Pseudorandomness490
    C.3.1ComputationalIndistinguishability490
    C.3.2PseudorandomGenerators491
    C.3.3PseudorandomFunctions492
    C.4Zero-Knowledge494
    C.4.1TheSimulationParadigm494
    C.4.2TheActualDefinition494
    C.4.3AGeneralResultandaGenericApplication495
    C.4.4DefinitionalVariationsandRelatedNotions497
    C.5EncryptionSchemes500
    C.5.1Definitions502
    C.5.2Constructions504
    C.5.3BeyondEavesdroppingSecurity505
    C.6SignaturesandMessageAuthentication507
    C.6.1Definitions508
    C.6.2Constructions509
    C.7GeneralCryptographicProtocols511
    C.7.1TheDefinitionalApproachandSomeModels512
    C.7.2SomeKnownResults517
    C.7.3ConstructionParadigmsandTwoSimpleProtocols517
    C.7.4ConcludingRemarks522

    AppendixD:ProbabilisticPreliminariesandAdvancedTopicsinRandomization523
    D.1ProbabilisticPreliminaries523
    D.1.1NotationalConventions523
    D.1.2ThreeInequalities524
    D.2Hashing528
    D.2.1Definitions528
    D.2.2Constructions529
    D.2.3TheLeftoverHashLemma529
    D.3Sampling533
    D.3.1FormalSetting533
    D.3.2KnownResults534
    D.3.3Hitters535
    D.4RandomnessExtractors536
    D.4.1DefinitionsandVariousPerspectives537
    D.4.2Constructions541
    AppendixE:ExplicitConstructions545
    E.1Error-CorrectingCodes546
    E.1.1BasicNotions546
    E.1.2AFewPopularCodes547
    E.1.3TwoAdditionalComputationalProblems551
    E.1.4AList-DecodingBound553
    E.2ExpanderGraphs554
    E.2.1DefinitionsandProperties555
    E.2.2Constructions561
    AppendixF:SomeOmittedProofs566
    F.1ProvingThatPHReducesto#P566
    F.2ProvingThatIP(f)?AM(O(f))?AM(f)572
    F.2.1EmulatingGeneralInteractiveProofsbyAM-Games572
    F.2.2LinearSpeedupforAM578
    AppendixG:SomeComputationalProblems583
    G.1Graphs583
    G.2BooleanFormulae585
    G.3FiniteFields,Polynomials,andVectorSpaces586
    G.4TheDeterminantandthePermanent587
    G.5PrimesandCompositeNumbers587
    Bibliography589
    Index601
  • 内容简介:
      复杂性理论是计算机科学的理论基础的核心。本书是著名计算机科学家OdedGoldreich的力作,书中对计算任务固有复杂性研究进行了概念性介绍,全面分析了复杂性理论的现代主题。
      本书涉及复杂性理论的很多子领域(如难度放大、伪随机性及概率证明系统等),涵盖了NP完整性、空间复杂性、随机性和计数、伪随机数生成器等内容,还在附录里面介绍了现代密码学基础等。
      本书内容严谨,可读性强,适合作为高年级本科生、研究生的教材。同时,书中展示了复杂性理论的很多子领域,也适合领域专家参考。
  • 作者简介:
      OdedGoldreich,以色列魏茨曼科学研究院(WeizmannInstituteofScience)计算机科学教授,MeyerW.Weisgal讲席教授。他是SIAMJournalonComputing、JournalofCryptology和ComputationalComplexity杂志的特约编辑。其主要研究方向是计算复杂性、随机性与计算以及密码学,他在这几个方面均有享誉世界的研究成果。作为一名活跃的学者,他发表了大量的论文,还著有两卷本的FoundationsofCryptography(《密码学基础》)和ModernCryptography,ProbabilisticProofsandPseudorandomness等专著。
  • 目录:
    1IntroductionandPreliminaries1
    1.1Introduction1
    1.1.1ABriefOverviewofComplexityTheory2
    1.1.2CharacteristicsofComplexityTheory6
    1.1.3ContentsofThisBook8
    1.1.4ApproachandStyleofThisBook12
    1.1.5StandardNotationsandOtherConventions16
    1.2ComputationalTasksandModels17
    1.2.1Representation18
    1.2.2ComputationalTasks18
    1.2.3UniformModels(Algorithms)20
    1.2.4Non-uniformModels(CircuitsandAdvice)36
    1.2.5ComplexityClasses42
    ChapterNotes43

    2P,NP,andNP-Completeness44
    2.1ThePVersusNPQuestion46
    2.1.1TheSearchVersion:FindingVersusChecking47
    2.1.2TheDecisionVersion:ProvingVersusVerifying50
    2.1.3EquivalenceoftheTwoFormulations54
    2.1.4TwoTechnicalCommentsRegardingNP55
    2.1.5TheTraditionalDefinitionofNP55
    2.1.6InSupportofPDifferentfromNP57
    2.1.7PhilosophicalMeditations58
    2.2Polynomial-TimeReductions58
    2.2.1TheGeneralNotionofaReduction59
    2.2.2ReducingOptimizationProblemstoSearchProblems61
    2.2.3Self-ReducibilityofSearchProblems63
    2.2.4DigestandGeneralPerspective67
    2.3NP-Completeness67
    2.3.1Definitions68
    2.3.2TheExistenceofNP-CompleteProblems69
    2.3.3SomeNaturalNP-CompleteProblems71
    2.3.4NPSetsThatAreNeitherinPnorNP-Complete81
    2.3.5ReflectionsonCompleteProblems85
    2.4ThreeRelativelyAdvancedTopics87
    2.4.1PromiseProblems87
    2.4.2OptimalSearchAlgorithmsforNP92
    2.4.3TheClasscoNPandItsIntersectionwithNP94
    ChapterNotes97
    Exercises99

    3VariationsonPandNP108
    3.1Non-uniformPolynomialTime(P/poly)108
    3.1.1BooleanCircuits109
    3.1.2MachinesThatTakeAdvice111
    3.2ThePolynomial-TimeHierarchy(PH)113
    3.2.1AlternationofQuantifiers114
    3.2.2Non-deterministicOracleMachines117
    3.2.3TheP/polyVersusNPQuestionandPH119
    ChapterNotes121
    Exercises122

    4MoreResources,MorePower127
    4.1Non-uniformComplexityHierarchies128
    4.2TimeHierarchiesandGaps129
    4.2.1TimeHierarchies129
    4.2.2TimeGapsandSpeedup136
    4.3SpaceHierarchiesandGaps139
    ChapterNotes139
    Exercises140

    5SpaceComplexity143
    5.1GeneralPreliminariesandIssues144
    5.1.1ImportantConventions144
    5.1.2OntheMinimalAmountofUsefulComputationSpace145
    5.1.3TimeVersusSpace146
    5.1.4CircuitEvaluation153
    5.2LogarithmicSpace153
    5.2.1TheClassL154
    5.2.2Log-SpaceReductions154
    5.2.3Log-SpaceUniformityandStrongerNotions155
    5.2.4UndirectedConnectivity155
    5.3Non-deterministicSpaceComplexity162
    5.3.1TwoModels162
    5.3.2NLandDirectedConnectivity164
    5.3.3ARetrospectiveDiscussion171
    5.4PSPACEandGames172
    ChapterNotes175
    Exercises175

    6RandomnessandCounting184
    6.1ProbabilisticPolynomialTime185
    6.1.1BasicModelingIssues186
    6.1.2Two-SidedError:TheComplexityClassBPP189
    6.1.3One-SidedError:TheComplexityClassesRPandcoRP193
    6.1.4Zero-SidedError:TheComplexityClassZPP199
    6.1.5RandomizedLog-Space199
    6.2Counting202
    6.2.1ExactCounting202
    6.2.2ApproximateCounting211
    6.2.3SearchingforUniqueSolutions217
    6.2.4UniformGenerationofSolutions220
    ChapterNotes227
    Exercises230

    7TheBrightSideofHardness241
    7.1One-WayFunctions242
    7.1.1GeneratingHardInstancesandOne-WayFunctions243
    7.1.2AmplificationofWeakOne-WayFunctions245
    7.1.3Hard-CorePredicates250
    7.1.4ReflectionsonHardnessAmplification255
    7.2HardProblemsinE255
    7.2.1AmplificationwithRespecttoPolynomial-SizeCircuits257
    7.2.2AmplificationwithRespecttoExponential-SizeCircuits270
    ChapterNotes277
    Exercises278

    8PseudorandomGenerators284
    Introduction285
    8.1TheGeneralParadigm288
    8.2General-PurposePseudorandomGenerators290
    8.2.1TheBasicDefinition291
    8.2.2TheArchetypicalApplication292
    8.2.3ComputationalIndistinguishability295
    8.2.4AmplifyingtheStretchFunction299
    8.2.5Constructions301
    8.2.6Non-uniformlyStrongPseudorandomGenerators304
    8.2.7StrongerNotionsandConceptualReflections305
    8.3DerandomizationofTime-ComplexityClasses307
    8.3.1DefiningCanonicalDerandomizers308
    8.3.2ConstructingCanonicalDerandomizers310
    8.3.3TechnicalVariationsandConceptualReflections313
    8.4Space-BoundedDistinguishers315
    8.4.1DefinitionalIssues316
    8.4.2TwoConstructions318
    8.5Special-PurposeGenerators325
    8.5.1PairwiseIndependenceGenerators326
    8.5.2Small-BiasGenerators329
    8.5.3RandomWalksonExpanders332
    ChapterNotes334
    Exercises337

    9ProbabilisticProofSystems349
    9.1InteractiveProofSystems352
    9.1.1MotivationandPerspective352
    9.1.2Definition354
    9.1.3ThePowerofInteractiveProofs357
    9.1.4VariantsandFinerStructure:AnOverview363
    9.1.5OnComputationallyBoundedProvers:AnOverview366
    9.2Zero-KnowledgeProofSystems368
    9.2.1DefinitionalIssues369
    9.2.2ThePowerofZero-Knowledge372
    9.2.3ProofsofKnowledge-AParentheticalSubsection378
    9.3ProbabilisticallyCheckableProofSystems380
    9.3.1Definition381
    9.3.2ThePowerofProbabilisticallyCheckableProofs383
    9.3.3PCPandApproximation398
    9.3.4MoreonPCPItself:AnOverview401
    ChapterNotes404
    Exercises406

    10RelaxingtheRequirements416
    10.1Approximation417
    10.1.1SearchorOptimization418
    10.1.2DecisionorPropertyTesting423
    10.2Average-CaseComplexity428
    10.2.1TheBasicTheory430
    10.2.2Ramifications442
    ChapterNotes451
    Exercises453

    Epilogue461
    AppendixA:GlossaryofComplexityClasses463
    A.1Preliminaries463
    A.2Algorithm-BasedClasses464
    A.2.1TimeComplexityClasses464
    A.2.2SpaceComplexityClasses467
    A.3Circuit-BasedClasses467

    AppendixB:OntheQuestforLowerBounds469
    B.1Preliminaries469
    B.2BooleanCircuitComplexity471
    B.2.1BasicResultsandQuestions472
    B.2.2MonotoneCircuits473
    B.2.3Bounded-DepthCircuits473
    B.2.4FormulaSize474
    B.3ArithmeticCircuits475
    B.3.1UnivariatePolynomials476
    B.3.2MultivariatePolynomials476
    B.4ProofComplexity478
    B.4.1LogicalProofSystems480
    B.4.2AlgebraicProofSystems480
    B.4.3GeometricProofSystems481

    AppendixC:OntheFoundationsofModernCryptography482
    C.1IntroductionandPreliminaries482
    C.1.1TheUnderlyingPrinciples483
    C.1.2TheComputationalModel485
    C.1.3OrganizationandBeyond486
    C.2ComputationalDifficulty487
    C.2.1One-WayFunctions487
    C.2.2Hard-CorePredicates489
    C.3Pseudorandomness490
    C.3.1ComputationalIndistinguishability490
    C.3.2PseudorandomGenerators491
    C.3.3PseudorandomFunctions492
    C.4Zero-Knowledge494
    C.4.1TheSimulationParadigm494
    C.4.2TheActualDefinition494
    C.4.3AGeneralResultandaGenericApplication495
    C.4.4DefinitionalVariationsandRelatedNotions497
    C.5EncryptionSchemes500
    C.5.1Definitions502
    C.5.2Constructions504
    C.5.3BeyondEavesdroppingSecurity505
    C.6SignaturesandMessageAuthentication507
    C.6.1Definitions508
    C.6.2Constructions509
    C.7GeneralCryptographicProtocols511
    C.7.1TheDefinitionalApproachandSomeModels512
    C.7.2SomeKnownResults517
    C.7.3ConstructionParadigmsandTwoSimpleProtocols517
    C.7.4ConcludingRemarks522

    AppendixD:ProbabilisticPreliminariesandAdvancedTopicsinRandomization523
    D.1ProbabilisticPreliminaries523
    D.1.1NotationalConventions523
    D.1.2ThreeInequalities524
    D.2Hashing528
    D.2.1Definitions528
    D.2.2Constructions529
    D.2.3TheLeftoverHashLemma529
    D.3Sampling533
    D.3.1FormalSetting533
    D.3.2KnownResults534
    D.3.3Hitters535
    D.4RandomnessExtractors536
    D.4.1DefinitionsandVariousPerspectives537
    D.4.2Constructions541
    AppendixE:ExplicitConstructions545
    E.1Error-CorrectingCodes546
    E.1.1BasicNotions546
    E.1.2AFewPopularCodes547
    E.1.3TwoAdditionalComputationalProblems551
    E.1.4AList-DecodingBound553
    E.2ExpanderGraphs554
    E.2.1DefinitionsandProperties555
    E.2.2Constructions561
    AppendixF:SomeOmittedProofs566
    F.1ProvingThatPHReducesto#P566
    F.2ProvingThatIP(f)?AM(O(f))?AM(f)572
    F.2.1EmulatingGeneralInteractiveProofsbyAM-Games572
    F.2.2LinearSpeedupforAM578
    AppendixG:SomeComputationalProblems583
    G.1Graphs583
    G.2BooleanFormulae585
    G.3FiniteFields,Polynomials,andVectorSpaces586
    G.4TheDeterminantandthePermanent587
    G.5PrimesandCompositeNumbers587
    Bibliography589
    Index601
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《剑桥非洲史·20世纪卷(1905—1940)》 《剑桥非洲史·20世纪卷(1940—1975)》(丛书2册)
安德鲁·罗伯茨;迈克尔·克劳德
计算复杂性
面具与乌托邦:墨西哥人民及其文化剪影
[墨]萨穆埃尔·拉莫斯
计算复杂性
苏联的外宾商店:为了工业化所需的黄金
[俄罗斯]叶列娜·亚历山德罗夫娜·奥金娜
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警治的终结
[英]亚历克斯·S.维塔莱 著;王飞、张鹏瀚 译
计算复杂性
用电影燃尽欲望
[【日】]园子温;余梦娇