Introduction to complexity theory, lecture notes

427 43 1MB

English Pages 375 Year 1999

Table of contents :
Table of Contents......Page 16
Lecture 1 - The P vs NP Question......Page 23
Lecture 2 - NP-completeness and Self Reducibility......Page 31
Lecture 3 - More on NP and some on DTIME......Page 45
Lecture 4 - Space Complexity......Page 57
Lecture 5 - Non-Deterministic Space......Page 65
Lecture 6 - Inside Non-Deterministic Logarithmic Space......Page 79
Lecture 7 - Randomized Computations......Page 95
Lecture 8 - Non-Uniform Polynomial Time......Page 113
Lecture 9 - The Polynomial Hierarchy (PH)......Page 123
Lecture 10 - The Counting Class #P......Page 137
Lecture 11 - Interactive Proof Systems......Page 157
Lecture 12 - Probabilistically Checkable Proof Systems......Page 171
Lecture 13 - Pseudorandom Generators......Page 187
Lecture 14 - Pseudorandomness and Computational Difficulty......Page 211
Lecture 15 - Derandomization of BPP......Page 221
Lecture 16 - Derandomizing Space-Bounded Computations......Page 235
Lecture 17 - Zero-Knowledge Proof Systems......Page 247
Lecture 18 - NP in PCP[poly, O(1)]......Page 269
Lecture 19 - DTIME vs DSPACE......Page 285
Lecture 20 - Circuit Depth and Space Complexity......Page 293
Lecture 21 - Communication Complexity......Page 305
Lecture 22 - Monotone Circuit Depth and Communication Complexity......Page 315
Lecture 23 - The FORK Game......Page 329
Lecture 24 - Average Case Complexity......Page 337
Lecture 25 - Computational Learning Theary......Page 349
Lecture 26 - Relativization......Page 365