Computational Complexity Theory

  1. Models of Computation
    1. Turing Machines
      1. Formal Definition
        1. Components and Structure
          1. Tape, Head, and States
            1. Transition Function
              1. Configuration and Computation
              2. Deterministic Turing Machines
                1. Definition and Properties
                  1. Acceptance and Rejection
                    1. Example Computations
                    2. Nondeterministic Turing Machines
                      1. Definition and Properties
                        1. Acceptance Criteria
                          1. Computation Trees
                          2. Multi-tape Turing Machines
                            1. Definition and Advantages
                              1. Simulation by Single-tape Machines
                              2. Universal Turing Machine
                                1. Definition and Significance
                                  1. Machine and Input Encoding
                                2. Alternative Computational Models
                                  1. Random Access Machines
                                    1. Register Machines
                                      1. Lambda Calculus
                                        1. Cellular Automata
                                        2. Church-Turing Thesis
                                          1. Statement and Significance
                                            1. Model Equivalence
                                              1. Physical Church-Turing Thesis
                                              2. Decidability Theory
                                                1. Decidable Languages
                                                  1. Definition and Examples
                                                  2. Recognizable Languages
                                                    1. Definition and Examples
                                                    2. Undecidable Problems
                                                      1. Halting Problem
                                                        1. Rice's Theorem
                                                          1. Reduction Techniques

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                                                      2. Mathematical Foundations

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                                                      4. Complexity Measurement