Computational Complexity Theory

  1. Interactive Proof Systems
    1. Interactive Computation Model
      1. Prover-Verifier Paradigm
        1. Roles and Capabilities
          1. Communication Protocols
          2. Completeness and Soundness
            1. Perfect Completeness
              1. Soundness Error
            2. Interactive Proof Classes
              1. Interactive Polynomial Time IP
                1. Definition and Properties
                  1. Round Complexity
                  2. Arthur-Merlin Games AM
                    1. Public Coin Protocols
                      1. Relationship to IP
                      2. Multi-Prover Interactive Proofs MIP
                        1. Definition and Power
                      3. Zero-Knowledge Proofs
                        1. Zero-Knowledge Property
                          1. Simulator Definition
                            1. Perfect, Statistical, Computational
                            2. Applications
                              1. Cryptographic Protocols
                                1. Authentication Systems
                                2. Examples
                                  1. Graph Isomorphism
                                    1. Quadratic Residuosity
                                  2. Major Results
                                    1. IP = PSPACE Theorem
                                      1. Statement and Significance
                                        1. Proof Outline
                                          1. Arithmetization Technique
                                          2. MIP = NEXP Theorem
                                            1. Statement and Implications

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                                        10. Randomized Complexity

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                                        12. Circuit Complexity