{"product_id":"theory-of-computational-complexity-hardback-9781118306086","title":"Theory of Computational Complexity (Hardback) 9781118306086","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTheory of Computational Complexity\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eDing-Zhu Du (Author), Ker-I Ko (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118306086, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 11 July 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e512 pages\u003cbr\u003e23.6 x 16.3 x 3.1 cm, 0.839 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\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\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\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\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand 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