Computational Complexity Theory

  1. Randomized Complexity
    1. Probabilistic Computation Models
      1. Probabilistic Turing Machines
        1. Definition and Operation
          1. Randomness as Resource
          2. Random Bit Generation
            1. Probability Distributions
            2. Randomized Complexity Classes
              1. Bounded-Error Probabilistic Polynomial Time BPP
                1. Definition and Properties
                  1. Error Probability Bounds
                    1. Amplification Techniques
                    2. Randomized Polynomial Time RP
                      1. Definition and Characterization
                        1. One-Sided Error
                        2. Co-Randomized Polynomial Time co-RP
                          1. Definition and Properties
                          2. Zero-Error Probabilistic Polynomial Time ZPP
                            1. Definition and Properties
                              1. Expected Runtime
                              2. Class Relationships
                                1. RP ∩ co-RP = ZPP
                                  1. BPP Containments
                                2. Randomized Algorithms
                                  1. Primality Testing
                                    1. Miller-Rabin Algorithm
                                      1. Solovay-Strassen Algorithm
                                      2. Polynomial Identity Testing
                                        1. Randomized Data Structures
                                        2. Derandomization
                                          1. Pseudorandom Generators
                                            1. Definition and Properties
                                              1. Cryptographic Generators
                                              2. Hardness versus Randomness
                                                1. Nisan-Wigderson Generator
                                                  1. Hardness Assumptions
                                                  2. Derandomization Techniques
                                                    1. Method of Conditional Expectations
                                                      1. Exhaustive Search

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                                                  9. Polynomial Hierarchy

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                                                  11. Interactive Proof Systems