For scribe notes, please use template.tex and macros.tex
For problem sets, feel free to start by modifying the source code (requires psheader.tex and macros.tex to compile).
Readings refer to chapters or sections of Computational Complexity: A Modern Approach, by Arora & Barak (1st ed).
| Date | Title | Notes/Handouts | Readings |
| Jan 25 | Overview and Model of Computation | Intro,0,1 | |
| Syllabus | html | ||
| Problem Set 0 (due 2/4) | |||
| Jan 27 | Hierarchy Theorems | 3.1,3.2 | |
| Feb 1 | Relations between Resources, P vs NP, Reductions, Boolean Circuits | 2,4.1,6.1 | |
| Feb 3 | P- and NP-completeness, Space Complexity: L, NL | 2,6.1,6.2,3.3, 4.1, 4.3.0 | |
| Problem Set 1 (due 2/18) | pdf tex | ||
| Feb 8 | Space Complexity: NL, PSPACE | 4.3, 4.2 | |
| Feb 10 | Alternation & the Polynomial Hierarchy | 5.0-5.3 | |
| Feb 17 | PH via Oracles & Time-Space Tradeoffs for SAT | 5.4-5.5 | |
| Problem Set 2 (due 3/4) | pdf tex | ||
| FRI Feb 19 | Provably Intractable Problems: EXP, NEXP, EXPSPACE | Sipser 9.1 (in solns dir on course website) |
|
| Feb 22,24 | No class | ||
| Mar 1 | Relativization, Basic Circuit Complexity: P/poly | 3.4, 6.0-6.4 | |
| Mar 3 | Circuit Depth: NC, AC | 6.5-6.7 | |
| FRI Mar 5 | More circuit depth, Randomized Computation: BPP, RP, ZPP | 7.0-7.4 | |
| Problem Set 3 (due 3/25) | pdf tex | ||
| Mar 8 | BPP in PH, BPP in P/poly, Promise Problems | 7.5 | |
| Mar 10 | Randomized Reductions: USAT, Counting: #P | 17.4.1,17.0-17.3.0 | |
| Mar 15,17 | No class (Spring Break) | ||
| Mar 22 | Counting: Valiant, Toda, PP, Approximate Counting | 17.3.1-17.4.0 | |
| Mar 24 | Approximate Counting, Uniform Sampling | 17.3.2 | |
| Problem Set 4 (due 4/8) | pdf tex | ||
| Mar 29 | Average-Case Complexity: Permanent, polynomial reconstruction | 8.6.2 (cf. 19.1,19.4.2) | |
| Mar 31 | Interactive Proofs: IP | 8.1, 8.3, | |
| Apr 5 | Variants of Interactive Proofs: AM, MA | 8.4, 8.6, 8.2 | |
| Apr 7 | AM vs. IP, AM vs. PH | 8.2 | |
| Problem Set 5 (due 4/22) | pdf tex | ||
| Apr 12 | PCPs and Hardness of Approximation | 11.0-11.3 | |
| Apr 14 | NP in PCP(poly(n),O(1)) | 11.5 | |
| Apr 19 | Linearity Testing, More Inapproximability | 11.4 | |
| Apr 21 | More Inapproximability, Algebraic Complexity: AlgP, AlgNP | 11.4, 16.1 | |
| Problem Set 6 (due 5/6) | |||
| Apr 26 | Algebraic Complexity: Perm vs. Det | 16.1 | |
| Apr 28 | Algebraic Circuit Lower Bounds | ||
| May 3 | Quantum Computation: QBP | 10.1, 10.2.0, 10.3 | |
| May 5 | Quantum Computation: Fourier Transform and Factoring | 10.6 |