Logic for Computer Science

  1. Logic and Computation
    1. Computability Theory
      1. Turing Machines
        1. Definition of Turing Machines
          1. Turing Machine Computations
            1. Encoding Logic in Turing Machines
            2. Recursive Functions
              1. Primitive Recursive Functions
                1. General Recursive Functions
                  1. Relationship to Logic
                  2. Decidability
                    1. Decidable Sets
                      1. Decidable Problems in Logic
                        1. Decision Procedures
                        2. Undecidability
                          1. Undecidable Problems
                            1. Reduction Techniques
                              1. Rice's Theorem
                              2. The Halting Problem
                                1. Statement of the Problem
                                  1. Proof of Undecidability
                                    1. Implications for Logic
                                    2. Church-Turing Thesis
                                      1. Statement and Interpretations
                                        1. Implications for Computation
                                      2. Complexity Theory
                                        1. Boolean Satisfiability Problem
                                          1. Definition and Variants
                                            1. 3-SAT Problem
                                              1. Importance in Computer Science
                                              2. Complexity Classes
                                                1. P Class
                                                  1. NP Class
                                                    1. Co-NP Class
                                                    2. NP-Completeness
                                                      1. Definition of NP-Complete
                                                        1. Cook-Levin Theorem
                                                          1. Reduction Techniques
                                                          2. The P vs NP Problem
                                                            1. Statement of the Problem
                                                              1. Implications for Logic and Computing
                                                              2. Other Complexity Results
                                                                1. PSPACE-Complete Problems
                                                                  1. Quantified Boolean Formulas

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                                                              4. First-Order Logic

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                                                              6. Applications in Hardware Design