Tentative Schedule
| 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 |