Lectures

Lectures

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 Tues Jan 18 Introduction, computational problems, computational model PDF Sipser Chap. 3,7; AB Chap. 0, 1.1-1.6; Papad. Chap. 2.1-2.5 sec. 3.0, 3.1
2 Thurs Jan 20 Time, space, nondeterminism, P, NP PDF Above, and Sipser 7.3, Papad. 2.7, AB Chap. 2
3 Tues Jan 25 Reductions, NP completeness PDF Sipser 7.4, 7.5, AB 2.2-2.4, Papad. ch 8,9
4 Thurs Jan 27 Ladner's theorem, polynomial hierarchy PDF AB 3.3, Cai 2.3-2.6, Papad. 17.2
5 Tues Feb 1 Polynomial hierarchy, oracles, nonuniformity PDF Cai 2.3-2.6, Papad. 17.2; Cai 4.1, 4.2, Papad. 4.3, 11.4; AB chapter 6
6 Thurs Feb 3 Circuit basics, P/poly, Karp-Lipton PDF the above and AB 6.4 (also Cai 4.2, Papad. 17.3)
7 Tues Feb 8 Karp-Lipton, Baker-Gill-Solovay, padding, start hierarchy theorems PDF AB 3.4, Cai 12.1, Papad. 20.1, Sipser 9.1, Papad. 7.1, 7.2
8 Thurs Feb 10 Clocked simulation, hierarchy theorems PDF Sipser 9.1, Papad. 7.1, 7.2
9 Tues Feb 15 Relations between different resources PDF Papad. 7.3
10 Thurs Feb 17 Space complexity, Savitch's theorem PDF AB Chap. 4, Sipser Chap. 8, Cai Chap. 3, Papad. 7.3
11 Tues Feb 22 NL-completeness, PSPACE-completeness PDF AB 4.2, Papad. 19.1, Sipser 8.3, Cai 3.4
12 Thurs Feb 24 PSPACE-completeness of QBF, GG PDF As above
13 Tues Feb 28 Immerman-Szelepcsényi theorem, probability basics PDF AB 4.3.2, Papad. 7.3, Sipser 8.6, Cai 3.3; Cai 5.1, Wikipedia
14 Thurs Mar 3 More probability basics, tail bounds, polynomial identity testing PDF Cai 3.3, Wikipedia, Papad. 11.1, AB 7.2.3
15 Tues Mar 8 Polynomial identity testing, randomized algorithm for 3CNF SAT PDF As above
16 Thurs Mar 10 Randomized algorithm for 3CNF SAT, randomized complexity classes PDF Papad. 11.2, AB 7.3, Cai 5.4
17 Tues Mar 22 Randomized complexity classes, amplification, relations among classes PDF Papad. 11.2, AB 7.4, 7.5, Cai 5.4, 5.5
18 Thurs Mar 24 BPP contained in P/poly (Adleman), BPP contained in 2nd level of hierarchy (Sipser/Gacs/Lautemann) PDF Papad. 11.2, AB 7.4, Cai 5.4
19 Tues Mar 29 Complexity of counting problems: basics, completeness PDF Papad. 18.1, AB 17.1-17.3
20 Thurs Mar 31 Permanent, random self-reducibility PDF Papad. 18.1, AB 17.1-17.3, AB 8.6.2
21 Tues April 5 Random self-reducibility of modular permanent, approximate counting PDF AB 8.6.2, AB 17.1.2
22 Thurs April 7 FPRAS for \#DNF, no FPRAS for \#CYCLES PDF AB 17.1.2
23 Tues April 12 Deterministic communication complexity of functions PDF AB 13.1, 13.2
24 Thurs April 14 Randomized communication complexity of functions, applications to TM lower bounds PDF AB 13.1, 13.2
25 Tues April 19 Circuit complexity: lower bounds for almost all functions, start constant-depth circuit lower bounds PDF AB 6.5, AB 14.1.0
26 Thurs April 21 Start lower bounds for constant-depth circuits with MAJ gate on top PDF This paper by Aspnes, Beigel, Furst, Rudich (sec 1.2 through Lemma 2.3)
27 Tues April 26 Lower bound for constant-depth circuits with MAJ gate on top PDF This paper by Aspnes, Beigel, Furst, Rudich (sec 5 through Lemma 5.4)
28 Thurs April 26 Finish lower bound for constant-depth circuits with MAJ gate on top, Subbotovskaya's lower bound for formulas based on random restrictions PDF

Schedule of Topics

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.