Date
|
Topic
|
Readings
|
Homework
|
|
Sep 3
|
Review of Turing machines; Hierarchy theorems.
|
Sections 3.1 and 9.1 of TC
|
|
Sep 8
|
Polynomial hierarchy.
|
Section 2.3 of LC
|
|
Sep 10
|
Oracle Turing machines; Sigma_2^P = NP^{SAT}
|
Sections 2.4 and 2.5 of LC
|
|
Sep 15
|
Circuits and sparse sets; Karp–Lipton theorem
|
Sections 4.1 and 4.2 of LC
|
|
Sep 17
|
Mahaney's theorem; PSPACE
|
Section 4.3 of LC and Section 8.1 of TC
|
|
Sep 22
|
PSPACE = NPSPACE
|
Sec 8.1 and 8.2 of TC
|
|
Sep 24
|
L, NL and coNL
|
Sec 8.4 and 8.6 of TC
|
|
Sep 29
|
NL = co-NL and PSPACE-completeness
|
Sec 8.6 and 8.3 of TC
|
|
Oct 1
|
NL-completeness and randomized algorithms
|
Sec 8.5 of TC and 5.2.2 of LC
|
|
Oct 6
|
Amplification of RP and BPP with tail bounds
|
Sec 5.1.1, 5.1.2, 5.1.3 and 5.4 of LC
|
|
Oct 8
|
BPP in \Sigma_2^P and Interactive Proof Systems
|
Sec 5.5 of LC
|
|
Oct 13
|
#SAT in IP
|
Sec 10.4 of TC
|
|
Oct 15
|
IP = PSPACE
|
Sec 10.4 of TC
|
|
Oct 20
|
Midterm
|
|
|
Oct 22
|
PCP Theorem
|
Sec 18.1 of MA
|
|
Oct 27
|
PCP Theorem
|
Sec 18.2 of MA
|
|
Oct 29
|
PCP Theorem
|
Sec 18.4 of MA
|
|
Nov 3
|
Academic Holiday
|
|
|
Nov 5
|
PCP Theorem
|
Sec 18.4 of MA
|
|
Nov 10
|
Communication complexity
|
Chapter 1 of CC
|
|
Nov 12
|
Lower bounds via monochromatic rectangles
|
Chapter 1 of CC
|
|
Nov 17
|
CC vs monochromatic partitions; rank
|
Chapter 1 and Pages 33-37 of CC
|
|
Nov 19
|
Randomized communication complexity
|
Sec 2.1, 2.2 and 2.4 of Notes by Shachar Lovett
|
|
Nov 24
|
Academic Holiday
|
|
|
Nov 26
|
Lower bounds for disjointness
|
Sec 4.3 of Notes by Shachar Lovett
|
|
Dec 1
|
Circuit depth and KW games
|
Pages 97-99 of CC
|
|
Dec 3
|
Monotone circuit depth lower bounds
|
Pages 99-101 of CC
|
|
Dec 8
|
TBA
|
|