Rocco's lecture notes will be posted soon after the class. You can also find course videos in the "Video Library" section of Courseworks soon after class.
Warning: the notes below were generated in real time and have not been edited. They may contain typos or other errors. They may also contain aesthetically displeasing color combinations.
| Number | Date | Topics | Notes | References |
|---|---|---|---|---|
| 1 | Wed Jan 18 | Introduction, computational problems, computational model | Sipser Chap. 3,7; AB Chap. 0, 1.1-1.6; Papad. Chap. 2.1-2.5 sec. 3.0, 3.1 | |
| 2 | Mon Jan 20 | Time, space, nondeterminism, P, NP | Above, and Sipser 7.3, Papad. 2.7, AB Chap. 2 | |
| 3 | Wed Jan 25 | Co-classes, reductions, NP completeness, Cook-Levin | Sipser 7.4, 7.5, AB 2.2-2.4, Papad. ch 8,9 | |
| 4 | Mon Jan 30 | Ladner's theorem, start polynomial hierarchy | AB 3.3, Cai 2.3-2.6, Papad. 17.2 | |
| 5 | Wed Feb 1 | Polynomial hierarchy, oracles | Cai 2.3-2.6, Papad. 17.2; Cai 4.1, 4.2, Papad. 4.3, 11.4; AB chapter 6 | |
| 6 | Mon Feb 3 | Nonuniformity, circuit basics, P/poly | the above | |
| 7 | Wed Feb 8 | Karp-Lipton, Baker-Gill-Solovay, padding | AB 6.4, Cai 4.2, Papad. 17.13 for Karp-Lipton AB 3.4, Cai 12.1 for Baker-Gill-Solovay | |
| 8 | Mon Feb 13 | Padding, clocked simulation, hierarchy theorems | Sipser 9.1, Papad. 7.1, 7.2, 20.1 | |
| 9 | Wed Feb 15 | Relations between different resources | Papad. 7.3 | |
| 10 | Mon Feb 20 | Space complexity, Savitch's theorem | AB Chap. 4, Sipser Chap. 8, Cai Chap. 3, Papad. 7.3 | |
| 11 | Wed Feb 22 | NL-completeness, PSPACE-completeness | AB 4.2, Papad. 19.1, Sipser 8.3, Cai 3.4 | |
| 12 | Mon Feb 27 | PSPACE-completeness of QBF, GG | As above | |
| 13 | Wed Feb 28 | Immerman-Szelepcsényi theorem, probability basics | AB 4.3.2, Papad. 7.3, Sipser 8.6, Cai 3.3; Cai 5.1, these notes on probability basics | |
| 14 | Mon Mar 6 | Tail bounds, randomized algorithm for polynomial identity testing | Cai 5.1, the above notes, Papad. 11.1 (see also Sipser 10.2), AB 7.2.3 | |
| 15 | Wed Mar 8 | Finish polynomial identity testing, randomized algorithm for 3CNF SAT, start randomized complexity classes | As above, Papad. 11.2, AB 7.3, Cai 5.4 | |
| 16 | Mon Mar 20 | Randomized complexity classes, amplification, relations among classes | Papad. 11.2, AB 7.3, Cai 5.4 | |
| 17 | Wed Mar 22 | Randomness versus nonuniformity, BPP and poly-time hierarchy, start counting | Papad. 11.2, AB 7.4, 7.5, Cai 5.4, 5.5 | |
| 18 | Mon Mar 29 | Complexity of counting problems: basics, completeness, permanent | Papad. 18.1, AB 17.1-17.3 | |
| 19 | Wed Mar 31 | Permanent, random self-reducibility | Papad. 18.1, AB 17.1-17.3, AB 8.6.2 | |
| 20 | Mon Apr 3 | Finish random self-reducibility of permanent, start approximate counting | As above | |
| 21 | Wed April 5 | FPRAS for #DNF, no FPRAS for #CYCLES, NP-oracle gives FPRAS for all of #P | AB 17.1.2 | |
| 22 | Mon April 10 | Deterministic communication complexity of functions: examples, rectangles, protocols | AB 13.1, 13.2 | |
| 23 | Wed April 12 | Randomized communication complexity, applications to TM lower bounds | AB 13.1, 13.2 | |
| 24 | Mon April 17 | Circuit complexity: lower bounds for almost all functions, start constant-depth circuit lower bounds | AB 6.5, AB 14.1.0 | 25 | Wed April 19 | Constant-depth circuit upper bounds, lower bounds based on switching lemma | AB 6.5, AB 14.1.0 | 26 | Mon April 24 | Start lower bound for constant-depth circuits with MAJ gate on top | This paper by Aspnes, Beigel, Furst, Rudich (sec 1.2 through Lemma 2.3, sec 5 through Lemma 5.4) | 27 | Wed April 26 | More lower bound for constant-depth circuits with MAJ gate on top | as above | 28 | Mon May 1 | Finish lower bound for constant-depth circuits with MAJ gate on top, Choose Your Own Adventure | as above | -->
Here is an anticipated list of topics. Note that the ordering of some subtopics may change, and we will often spend more (but sometimes less) than one lecture per topic.