Preface |
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ix | |
Notes on the Second Edition |
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xv | |
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Part I Uniform Complexity |
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1 | (148) |
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1 Models of Computation and Complexity Classes |
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3 | (42) |
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1.1 Strings, Coding, and Boolean Functions |
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3 | (4) |
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1.2 Deterministic Turing Machines |
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7 | (7) |
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1.3 Nondeterministic Turing Machines |
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14 | (4) |
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18 | (7) |
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1.5 Universal Turing Machine |
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25 | (4) |
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29 | (4) |
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33 | (12) |
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38 | (5) |
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43 | (2) |
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45 | (36) |
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45 | (4) |
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49 | (5) |
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2.3 More NP-Complete Problems |
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54 | (7) |
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2.4 Polynomial-Time Turing Reducibility |
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61 | (7) |
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2.5 NP-Complete Optimization Problems |
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68 | (13) |
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76 | (3) |
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79 | (2) |
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3 The Polynomial-Time Hierarchy and Polynomial Space |
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81 | (38) |
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3.1 Nondeterministic Oracle Turing Machines |
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81 | (2) |
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3.2 Polynomial-Time Hierarchy |
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83 | (5) |
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3.3 Complete Problems in PH |
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88 | (7) |
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3.4 Alternating Turing Machines |
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95 | (5) |
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3.5 PSPACE-Complete Problems |
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100 | (8) |
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3.6 EXP-Complete Problems |
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108 | (11) |
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114 | (3) |
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117 | (2) |
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119 | (30) |
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4.1 Incomplete Problems in NP |
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119 | (3) |
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4.2 One-Way Functions and Cryptography |
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122 | (7) |
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129 | (2) |
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4.4 Unrelativizable Proof Techniques |
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131 | (1) |
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131 | (1) |
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4.6 Positive Relativization |
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132 | (3) |
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135 | (5) |
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4.8 Structure of Relativized NP |
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140 | (9) |
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144 | (3) |
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147 | (2) |
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Part II Nonuniform Complexity |
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149 | (146) |
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151 | (49) |
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5.1 Graphs and Decision Trees |
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151 | (6) |
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157 | (4) |
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161 | (5) |
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5.4 Monotone Graph Properties |
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166 | (2) |
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5.5 Topological Criterion |
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168 | (7) |
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5.6 Applications of the Fixed Point Theorems |
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175 | (4) |
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5.7 Applications of Permutation Groups |
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179 | (3) |
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5.8 Randomized Decision Trees |
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182 | (5) |
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187 | (13) |
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194 | (4) |
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198 | (2) |
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200 | (52) |
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200 | (4) |
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6.2 Polynomial-Size Circuits |
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204 | (6) |
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210 | (9) |
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6.4 Circuits with Modulo Gates |
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219 | (3) |
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222 | (6) |
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228 | (7) |
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235 | (7) |
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6.8 Random Circuits and RNC |
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242 | (10) |
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246 | (3) |
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249 | (3) |
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7 Polynomial-Time Isomorphism |
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252 | (43) |
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7.1 Polynomial-Time Isomorphism |
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252 | (4) |
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256 | (5) |
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7.3 Density of NP-Complete Sets |
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261 | (10) |
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7.4 Density of EXP-Complete Sets |
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271 | (4) |
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7.5 One-Way Functions and Isomorphism in EXP |
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275 | (10) |
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7.6 Density of P-Complete Sets |
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285 | (10) |
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289 | (3) |
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292 | (3) |
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Part III Probabilistic Complexity |
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295 | (163) |
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8 Probabilistic Machines and Complexity Classes |
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297 | (35) |
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8.1 Randomized Algorithms |
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297 | (5) |
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8.2 Probabilistic Turing Machines |
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302 | (3) |
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8.3 Time Complexity of Probabilistic Turing Machines |
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305 | (4) |
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8.4 Probabilistic Machines with Bounded Errors |
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309 | (3) |
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312 | (3) |
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315 | (3) |
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8.7 BPP and the Polynomial-Time Hierarchy |
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318 | (3) |
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8.8 Relativized Probabilistic Complexity Classes |
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321 | (11) |
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327 | (3) |
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330 | (2) |
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332 | (34) |
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333 | (3) |
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336 | (10) |
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9.3 P and the Polynomial-Time Hierarchy |
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346 | (6) |
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9.4 #P and the Polynomial-Time Hierarchy |
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352 | (2) |
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9.5 Circuit Complexity and Relativized P and #P |
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354 | (4) |
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9.6 Relativized Polynomial-Time Hierarchy |
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358 | (8) |
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361 | (3) |
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364 | (2) |
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10 Interactive Proof Systems |
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366 | (41) |
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10.1 Examples and Definitions |
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366 | (9) |
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10.2 Arthur--Merlin Proof Systems |
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375 | (4) |
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10.3 AM Hierarchy Versus Polynomial-Time Hierarchy |
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379 | (8) |
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387 | (9) |
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396 | (11) |
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402 | (4) |
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406 | (1) |
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11 Probabilistically Checkable Proofs and NP-Hard Optimization Problems |
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407 | (51) |
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11.1 Probabilistically Checkable Proofs |
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407 | (4) |
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11.2 PCP Characterization of NP |
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411 | (26) |
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414 | (4) |
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418 | (10) |
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428 | (9) |
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11.3 Probabilistic Checking and Inapproximability |
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437 | (3) |
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11.4 More NP-Hard Approximation Problems |
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440 | (18) |
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452 | (3) |
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455 | (3) |
References |
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458 | (22) |
Index |
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480 | |