Introduction | 1 | Sipser (2005) | |

Set Thoery, Sequences, Tuples, Functions, Relations and Graphs | 2 | do. | |

Turing Machine and its Language | 3 | do. | |

Designing Turing Machines | 4 | do. | |

Variants of Turing Machines | 5 | do. | |

Enumerators, Dovetailing, The Church-Turing Thesis, Hilbert's Tenth Problem | 6 | do. | |

Decidable Languages, The Acceptance Problem for DFAs | 7 | do. | |

The Halting Problem, Universal TM | 8 | do. | |

Undicidability of the Halting Problem | 9 | do. | |

Linear Bounded Automata, Computation Histories, Context Free Grammars | 10 | do. | |

Russell's Paradox, Emptiness Problem | 11 | do. | |

Post Correspondence Problem, Computable Functions | 12 | do. | |

Computable Functions (Cont.), Reducibility | 13 | do. | |

Reducibility (Cont.), Recursion Theorem | 14 | do. | |

Recursion Theorem (Cont.), Logical Theories | 15 | do. | |

Logical Theories (Cont.) | 16 | do. | |

Logical Theories (Cont.), Godel's Theorem | 17 | do. | |

Oracles, Turing Reducibility | 18 | do. | |

A definition of Information, Incompressible Strings | 19 | do. | |

Incompressible Strings (Cont.), Complexity Theory | 20 | do. | |

Big Oh and Little Oh Notations, Time Complexity | 21 | do. | |

Non-Deterministic Time, The Class P, The Class NP | 22 | do. | |

The Class NP (Cont.), Polynomial Time Verifiers | 23 | do. | |

The Class NP (Cont.) | 24 | do. | |

Subset Sum Problem, Satisfiability | 25 | do. | |

Satisfiability (Cont.), 3-Color | 26 | do. | |

Satisfiability (Cont.) | 27 | do. | |

The Cook-Levin Theorem | 28 | do. | |

NP-Completeness, Independent Sets | 29 | do. | |

Independent Sets (Cont.), NP-Completeness (Cont.), Clique, Vertex Cover | 30 | do. | |

Hamiltonian Path Problem | 31 | do. | |

NP-Completeness (Cont.) | 32 | do. | |

The Subset Sum Problem | 33 | do. | |

The Traveling Salesman Problem | 34 | do. | |

An Approximation Algorithm for TSP Problem | 35 | do. | |

Space Complexity | 36 | do. | |

Space Complexity (Cont.) | 37 | do. | |

Relationship between Space and Time Complexity, PSPACE-Completeness | 38 | do. | |

TQBF, Prove that TQBF is PSPACE-Complete | 39 | do. | |

TQBF (Cont.), FORMULA-GAME, Generalized Geography | 40 | do. | |

Generalized Geography (Cont.) | 41 | do. | |

LOGSPACE Transducer | 42 | do. | |

Prove the Theorem: NL = co-NL | 43 | do. | |

Prove the Theorem: NL = co-NL (Cont.) | 44 | do. | |

Overview of the course covered | 45 | do. | |