Date
|
Topic
|
Readings
|
Homework
|
|
Sep 7
|
Review of Turing machines; Hierarchy theorems.
|
Sections 3.1 and 9.1 of TC
|
|
Sep 12
|
Polynomial hierarchy.
|
Section 2.3 of LC
|
|
Sep 14
|
Oracle Turing machines; Sigma_2^P = NP^{SAT}
|
Sections 2.4 and 2.5 of LC
|
|
Sep 19
|
Circuits and sparse sets; Karp–Lipton theorem
|
Sections 4.1 and 4.2 of LC
|
|
Sep 21
|
Mahaney's theorem; PSPACE
|
Section 4.3 of LC and Section 8.1 of TC
|
|
Sep 26
|
PSPACE = NPSPACE
|
Sec 8.1 and 8.2 of TC
|
|
Sep 28
|
L, NL and coNL
|
Sec 8.4 and 8.6 of TC
|
|
Oct 3
|
NL = co-NL and PSPACE-completeness
|
Sec 8.6 and 8.3 of TC
|
|
Oct 5
|
NL-completeness and randomized algorithms
|
Sec 8.5 of TC and 5.2.2 of LC
|
|
Oct 10
|
Amplification of RP and BPP with tail bounds
|
Sec 5.1.1, 5.1.2, 5.1.3 and 5.4 of LC
|
|
Oct 12
|
BPP in \Sigma_2^P and Interactive Proof Systems
|
Sec 5.5 of LC
|
|
Oct 17
|
#SAT in IP
|
Sec 10.4 of TC
|
|
Oct 19
|
Midterm
|
|
|
Oct 24
|
IP = PSPACE
|
Sec 10.4 of TC
|
|
Oct 26
|
PCP Theorem
|
Sec 18.1 of MA
|
|
Oct 31
|
PCP Theorem
|
Sec 18.2 of MA
|
|
Nov 2
|
PCP Theorem
|
Sec 18.4 of MA
|
|
Nov 7
|
Academic Holiday
|
|
|
Nov 9
|
PCP Theorem
|
Sec 18.4 of MA
|
|
Nov 14
|
Communication complexity
|
Chapter 1 of CC
|
|
Nov 16
|
Lower bounds via monochromatic rectangles
|
Chapter 1 of CC
|
|
Nov 21
|
CC vs monochromatic partitions; rank
|
Chapter 1 and Pages 33-37 of CC
|
|
Nov 23
|
Academic Holiday
|
|
|
Nov 28
|
Randomized communication complexity
|
Sec 2.1, 2.2 and 2.4 of Notes by Shachar Lovett
|
|
Nov 30
|
Lower bounds for disjointness
|
Sec 4.3 of Notes by Shachar Lovett
|
|
Dec 5
|
Circuit depth and KW games
|
Pages 97-99 of CC
|
|
Dec 7
|
Monotone circuit depth lower bounds
|
Pages 99-101 of CC
|
|
Dec 12
|
|
|