{"product_id":"theory-of-computational-complexity-isbn-9781118306086","title":"Theory of Computational Complexity","description":"\u003cp\u003e\u003cb\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\"... complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity.\"\u003cbr\u003e—\u003cb\u003e\u003ci\u003eZentralblatt MATH\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA thorough revision based on advances in the field of computational complexity and readers’ feedback, the \u003ci\u003eSecond Edition\u003c\/i\u003e of \u003ci\u003eTheory of Computational Complexity\u003c\/i\u003e presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered.\u003c\/p\u003e \u003cp\u003eMaintaining extensive and detailed coverage, \u003ci\u003eTheory of Computational Complexity, Second Edition\u003c\/i\u003e, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The \u003ci\u003eSecond Edition\u003c\/i\u003e also features recent developments on areas such as NP-completeness theory, as well as:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science\u003c\/li\u003e \u003cli\u003eAdditional exercises at varying levels of difficulty to further test comprehension of the presented material\u003c\/li\u003e \u003cli\u003eEnd-of-chapter literature reviews that summarize each topic and offer additional sources for further study \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eTheory of Computational Complexity, Second Edition\u003c\/i\u003e, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.\u003c\/p\u003e \u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003eNotes on the Second Edition xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Uniform Complexity 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Models of Computation and Complexity Classes 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Strings, Coding, and Boolean Functions 3\u003c\/p\u003e \u003cp\u003e1.2 Deterministic Turing Machines 7\u003c\/p\u003e \u003cp\u003e1.3 Nondeterministic Turing Machines 14\u003c\/p\u003e \u003cp\u003e1.4 Complexity Classes 18\u003c\/p\u003e \u003cp\u003e1.5 Universal Turing Machine 25\u003c\/p\u003e \u003cp\u003e1.6 Diagonalization 29\u003c\/p\u003e \u003cp\u003e1.7 Simulation 33\u003c\/p\u003e \u003cp\u003eExercises 38\u003c\/p\u003e \u003cp\u003eHistorical Notes 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 NP-Completeness 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Np 45\u003c\/p\u003e \u003cp\u003e2.2 Cook’s Theorem 49\u003c\/p\u003e \u003cp\u003e2.3 More NP-Complete Problems 54\u003c\/p\u003e \u003cp\u003e2.4 Polynomial-Time Turing Reducibility 61\u003c\/p\u003e \u003cp\u003e2.5 NP-Complete Optimization Problems 68\u003c\/p\u003e \u003cp\u003eExercises 76\u003c\/p\u003e \u003cp\u003eHistorical Notes 79\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Polynomial-Time Hierarchy and Polynomial Space 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Nondeterministic Oracle Turing Machines 81\u003c\/p\u003e \u003cp\u003e3.2 Polynomial-Time Hierarchy 83\u003c\/p\u003e \u003cp\u003e3.3 Complete Problems in PH 88\u003c\/p\u003e \u003cp\u003e3.4 Alternating Turing Machines 95\u003c\/p\u003e \u003cp\u003e3.5 PSPACE-Complete Problems 100\u003c\/p\u003e \u003cp\u003e3.6 EXP-Complete Problems 108\u003c\/p\u003e \u003cp\u003eExercises 114\u003c\/p\u003e \u003cp\u003eHistorical Notes 117\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Structure of NP 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Incomplete Problems in NP 119\u003c\/p\u003e \u003cp\u003e4.2 One-Way Functions and Cryptography 122\u003c\/p\u003e \u003cp\u003e4.3 Relativization 129\u003c\/p\u003e \u003cp\u003e4.4 Unrelativizable Proof Techniques 131\u003c\/p\u003e \u003cp\u003e4.5 Independence Results 131\u003c\/p\u003e \u003cp\u003e4.6 Positive Relativization 132\u003c\/p\u003e \u003cp\u003e4.7 Random Oracles 135\u003c\/p\u003e \u003cp\u003e4.8 Structure of Relativized NP 140\u003c\/p\u003e \u003cp\u003eExercises 144\u003c\/p\u003e \u003cp\u003eHistorical Notes 147\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Nonuniform Complexity 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Decision Trees 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Graphs and Decision Trees 151\u003c\/p\u003e \u003cp\u003e5.2 Examples 157\u003c\/p\u003e \u003cp\u003e5.3 Algebraic Criterion 161\u003c\/p\u003e \u003cp\u003e5.4 Monotone Graph Properties 166\u003c\/p\u003e \u003cp\u003e5.5 Topological Criterion 168\u003c\/p\u003e \u003cp\u003e5.6 Applications of the Fixed Point Theorems 175\u003c\/p\u003e \u003cp\u003e5.7 Applications of Permutation Groups 179\u003c\/p\u003e \u003cp\u003e5.8 Randomized Decision Trees 182\u003c\/p\u003e \u003cp\u003e5.9 Branching Programs 187\u003c\/p\u003e \u003cp\u003eExercises 194\u003c\/p\u003e \u003cp\u003eHistorical Notes 198\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Circuit Complexity 200\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Boolean Circuits 200\u003c\/p\u003e \u003cp\u003e6.2 Polynomial-Size Circuits 204\u003c\/p\u003e \u003cp\u003e6.3 Monotone Circuits 210\u003c\/p\u003e \u003cp\u003e6.4 Circuits with Modulo Gates 219\u003c\/p\u003e \u003cp\u003e6.5 Nc 222\u003c\/p\u003e \u003cp\u003e6.6 Parity Function 228\u003c\/p\u003e \u003cp\u003e6.7 P-Completeness 235\u003c\/p\u003e \u003cp\u003e6.8 Random Circuits and RNC 242\u003c\/p\u003e \u003cp\u003eExercises 246\u003c\/p\u003e \u003cp\u003eHistorical Notes 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Polynomial-Time Isomorphism 252\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Polynomial-Time Isomorphism 252\u003c\/p\u003e \u003cp\u003e7.2 Paddability 256\u003c\/p\u003e \u003cp\u003e7.3 Density of NP-Complete Sets 261\u003c\/p\u003e \u003cp\u003e7.4 Density of EXP-Complete Sets 271\u003c\/p\u003e \u003cp\u003e7.5 One-Way Functions and Isomorphism in EXP 275\u003c\/p\u003e \u003cp\u003e7.6 Density of P-Complete Sets 285\u003c\/p\u003e \u003cp\u003eExercises 289\u003c\/p\u003e \u003cp\u003eHistorical Notes 292\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Probabilistic Complexity 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Probabilistic Machines and Complexity Classes 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Randomized Algorithms 297\u003c\/p\u003e \u003cp\u003e8.2 Probabilistic Turing Machines 302\u003c\/p\u003e \u003cp\u003e8.3 Time Complexity of Probabilistic Turing Machines 305\u003c\/p\u003e \u003cp\u003e8.4 Probabilistic Machines with Bounded Errors 309\u003c\/p\u003e \u003cp\u003e8.5 BPP and P 312\u003c\/p\u003e \u003cp\u003e8.6 BPP and NP 315\u003c\/p\u003e \u003cp\u003e8.7 BPP and the Polynomial-Time Hierarchy 318\u003c\/p\u003e \u003cp\u003e8.8 Relativized Probabilistic Complexity Classes 321\u003c\/p\u003e \u003cp\u003eExercises 327\u003c\/p\u003e \u003cp\u003eHistorical Notes 330\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Complexity of Counting 332\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Counting Class #P 333\u003c\/p\u003e \u003cp\u003e9.2 #P-Complete Problems 336\u003c\/p\u003e \u003cp\u003e9.3 ⊕P and the Polynomial-Time Hierarchy 346\u003c\/p\u003e \u003cp\u003e9.4 #P and the Polynomial-Time Hierarchy 352\u003c\/p\u003e \u003cp\u003e9.5 Circuit Complexity and Relativized ⊕P and #P 354\u003c\/p\u003e \u003cp\u003e9.6 Relativized Polynomial-Time Hierarchy 358\u003c\/p\u003e \u003cp\u003eExercises 361\u003c\/p\u003e \u003cp\u003eHistorical Notes 364\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Interactive Proof Systems 366\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Examples and Definitions 366\u003c\/p\u003e \u003cp\u003e10.2 Arthur–Merlin Proof Systems 375\u003c\/p\u003e \u003cp\u003e10.3 AM Hierarchy Versus Polynomial-Time Hierarchy 379\u003c\/p\u003e \u003cp\u003e10.4 IP Versus AM 387\u003c\/p\u003e \u003cp\u003e10.5 IP Versus PSPACE 396\u003c\/p\u003e \u003cp\u003eExercises 402\u003c\/p\u003e \u003cp\u003eHistorical Notes 406\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Probabilistically Checkable Proofs and NP-Hard Optimization Problems 407\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Probabilistically Checkable Proofs 407\u003c\/p\u003e \u003cp\u003e11.2 PCP Characterization of NP 411\u003cbr\u003e\u003cbr\u003e 11.2.1 Expanders 414\u003cbr\u003e\u003cbr\u003e 11.2.2 Gap Amplification 418\u003cbr\u003e\u003cbr\u003e 11.2.3 Assignment Tester 428\u003c\/p\u003e \u003cp\u003e11.3 Probabilistic Checking and Inapproximability 437\u003c\/p\u003e \u003cp\u003e11.4 More NP-Hard Approximation Problems 440\u003c\/p\u003e \u003cp\u003eExercises 452\u003c\/p\u003e \u003cp\u003eHistorical Notes 455\u003c\/p\u003e \u003cp\u003eReferences 458\u003c\/p\u003e \u003cp\u003eIndex 480\u003c\/p\u003e \u003cp\u003e\u003cb\u003eDING-ZHU DU, PhD\u003c\/b\u003e, is Professor in the Department of Computer Science at the University of Texas at Dallas. He has published over 180 journal articles in his areas of research interest, which include design and analysis of approximation algorithms for combinatorial optimization problems and communication networks. Dr. Du is also the coauthor of \u003ci\u003eProblem Solving in Automata, Languages, and Complexity\u003c\/i\u003e, also published by Wiley.\u003c\/p\u003e \u003cb\u003eKER-I KO, PhD\u003c\/b\u003e, is Professor in the Department of Computer Science at National Chiao Tung University, Taiwan. He has published extensively in his areas of research interest, which include computational complexity theory and its applications to numerical computation. Dr. Ko is also the coauthor of \u003ci\u003eProblem Solving in Automata, Languages, and Complexity\u003c\/i\u003e, also published by Wiley.  \u003cp\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\"...complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity.\" -\u003ci\u003eZentralblatt MATH\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eA thorough revision based on advances in the field of computational complexity and readers’ feedback, the \u003ci\u003eSecond Edition\u003c\/i\u003e of \u003ci\u003eTheory of Computational Complexity\u003c\/i\u003e presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered.\u003c\/p\u003e \u003cp\u003eMaintaining extensive and detailed coverage, \u003ci\u003eTheory of Computational Complexity, Second Edition\u003c\/i\u003e examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The \u003ci\u003eSecond Edition\u003c\/i\u003e also features recent developments on areas such as NP-completeness theory, as well as:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science\u003c\/li\u003e \u003cli\u003eAdditional exercises at varying levels of difficulty to further test comprehension of the presented material\u003c\/li\u003e \u003cli\u003eEnd-of-chapter literature reviews that summarize each topic and offer additional sources for further study\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eTheory of Computational Complexity, Second Edition\u003c\/i\u003e is an excellent textbook for courses on computational theory and complexity at the graduate-level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990381248741,"sku":"NP9781118306086","price":144.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118306086.jpg?v=1761787595","url":"https:\/\/k12savings.com\/products\/theory-of-computational-complexity-isbn-9781118306086","provider":"K12savings","version":"1.0","type":"link"}