**Tentative Schedule**

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Topic |
Dates |
Reading |

Overview | Feb 2 | Goldreich "Brief Overview" |

The Computational Model, Time Hierarchy Theorem | Feb 2 | Arora Chapter 1, Goldreich "Prelims" up to 3.4 |

Hierarchy Theorems, Relations between Resources | Feb 7-9 | Arora 4.1-4.3, Goldreich "More Resources, More Power" |

P vs NP (review), Reductions, Completeness | Feb 14 | Arora Chapter 2, Goldreich "P, NP, NP-Completeness" |

Circuits, P-completeness, NP-completeness | Feb 16 | Arora Chapter 2, Goldreich "P, NP, NP-Completeness" |

Space complexity: Logspace, NL | Feb 21 | Arora Chapter 3, Goldreich "Space Complexity" |

PSPACE, Alternation | Feb 23 | Arora Ch. 3.1,5.1. Goldreich "Space Complexity" Sec 4 |

The Polynomial Hierarchy | Feb 28 | Arora 5.0, Goldreich "On P/poly and PH" Sec 2 |

Time-Space Tradeoffs for SAT | Mar 2 | Not in either book |

No Lecture | Mar 7 | |

Provable Intractable Problems. EXP, NEXP, EXPSPACE | Mar 9 | Handout (Sipser 9.1) |

Relativization, Basic circuit complexity | Mar 14 | Arora 4.4, 6.0-6.2 |

Randomized Computation, BPP, RP | Mar 16 | Arora Chapter 7, Goldreich "Randomized Complexity Classes" |

Promise problems, complete problems for prBPP | Mar 21 | Arora Chapter 7, Goldreich "Randomized Complexity Classes" |

Unique SAT, counting problems | Mar 23 | Arora Chapter 8, Goldreich "Counting Problems" |

Toda's Theorem, #P-completeness of the permanent | Apr 4 | Arora Chapter 8, Goldreich "Counting Problems" |

Approximate counting, Average-case complexity | Apr 6 | Arora 17.3 |

Average-case complexity: permanent, polynomial reconstruction, multilinear extensions | Apr 11 | Arora 17.3 |

Interactive proofs, P^{#P} is in IP | Apr 13 | Arora Chapter 10, Goldreich "Probabilistic Proof Systems" |

Arthur-Merlin games: AM, MA | Apr 18 | Arora Chapter 10, Goldreich "Probabilistic Proof Systems" |

Multiple prover IP, PCP, Complexity of Approximation problems | Apr 20 | Goldreich "Probabilistic Proof Systems" |

More hardness of approximation problems, NP in PCP[poly,O(1)] | Apr 25 | Arora Chapter 19, Goldreich "Probabilistic Proof Systems" |

Linearity Testing, overview of proof of PCP theorem | Apr 27 | Arora Chapter 19, Goldreich "Probabilistic Proof Systems" |

Circuit depth | May 2 | Arora 6.3 |

Parity is not in AC0 | May 4 | Arora 14.1 |

Quantum computation | May 9 | Arora Chapter 21 |

Factoring in polytime on a quantum computer | May 11 | Arora Chapter 21 |

Conclusions | May 16 |

- S. Arora. Computational Complexity: A Modern Approach, a first (and not entirely finished) draft of a forthcoming text.
- O. Goldreich. Complexity Theory - Expositions, a set of on-line lecture notes.

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