Computational Complexity Theory

  1. Space Complexity Theory
    1. Space Complexity Fundamentals
      1. Space Measurement Models
        1. Work Tape Model
          1. Read-Only Input
          2. Space-Constructible Functions
          3. Logarithmic Space Classes
            1. Deterministic Logarithmic Space L
              1. Definition and Examples
                1. Reachability Problems
                2. Nondeterministic Logarithmic Space NL
                  1. Definition and Examples
                    1. Graph Connectivity
                  2. Polynomial Space Classes
                    1. Polynomial Space PSPACE
                      1. Definition and Examples
                        1. Game Problems
                        2. Nondeterministic Polynomial Space NPSPACE
                          1. Definition and Relationship to PSPACE
                        3. Exponential Space Classes
                          1. Exponential Space EXPSPACE
                            1. Definition and Examples
                          2. Space-Time Relationships
                            1. Inclusion Relationships
                              1. L ⊆ NL ⊆ P ⊆ NP ⊆ PSPACE
                              2. Separation Results
                                1. Open Problems
                                2. Key Space Complexity Theorems
                                  1. Savitch's Theorem
                                    1. Statement: PSPACE = NPSPACE
                                      1. Proof Technique
                                        1. Implications
                                        2. Immerman-Szelepcsényi Theorem
                                          1. Statement: NL = co-NL
                                            1. Proof Technique
                                              1. Significance
                                            2. PSPACE-Completeness
                                              1. Definition and Proof Techniques
                                                1. Quantified Boolean Formulas
                                                  1. QBF Problem
                                                    1. Alternating Quantifiers
                                                    2. Game Theory Applications
                                                      1. Two-Player Games
                                                        1. Geography Game
                                                          1. Generalized Game Problems

                                                      Previous

                                                      6. Reducibility and NP-Completeness

                                                      Go to top

                                                      Next

                                                      8. Hierarchy Theorems