Computational Complexity Theory

  1. Circuit Complexity
    1. Boolean Circuit Model
      1. Circuit Components
        1. Logic Gates
          1. Wires and Connections
          2. Circuit Parameters
            1. Size and Depth
              1. Fan-in and Fan-out
              2. Circuit Evaluation
              3. Circuit Families
                1. Uniform Circuit Families
                  1. Polynomial-Time Uniformity
                    1. Logspace Uniformity
                    2. Non-uniform Circuit Families
                      1. Arbitrary Circuit Families
                      2. Size and Depth Hierarchies
                      3. Non-uniform Complexity Classes
                        1. P/poly Class
                          1. Definition and Properties
                            1. Advice Strings
                              1. Relationship to Uniform Classes
                              2. Circuit Lower Bounds
                                1. Known Results
                                  1. Limitations and Barriers
                                  2. Natural Proofs Barrier
                                    1. Razborov-Rudich Theorem
                                      1. Implications for Lower Bounds
                                    2. Specific Circuit Classes
                                      1. AC⁰ Circuits
                                        1. Constant Depth, Polynomial Size
                                          1. Parity Lower Bounds
                                          2. NC Hierarchy
                                            1. Polylog Depth Circuits
                                              1. Parallel Computation

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                                          13. Quantum Complexity