John H. Reif
Spring Semester, 2009
Classes: Wend,
Fri: 1:00 PM North 306
Recitations:
Mon 1:00 PM North 314
Class |
Date |
Topics |
Primary Lecture Notes |
Secondary Lecture Notes |
Primary Textbook Readings |
Secondary Textbook Readings |
Handouts |
1 |
Jan
9 North
306 |
Introduction: Turing
Machines, |
[T,
Ch1] [T,
Ch2] [T,
Ch3] [T,
Ch4] |
[Arora] [Beame] [Spielman] [Trevisan] |
[AB, Ch 1] [G, Ch1] |
[HMU,
Ch 8] |
|
2 |
Jan
12 North
306 |
P
and NP-Completeness: P,
NP, NP-Completeness NP-Completeness
via Reductions |
[T,
Ch5] [T,
Ch7] [T, Ch8]
|
[Arora] [Spielman] |
[AB, Ch 2] [G, Ch2] |
[G, AppA] [GJ, Ch3,4] [HMU,
Ch10] |
|
3 |
Jan
14 North 306 |
Recitation:
Polynomial
Hierarchy (PH): Properties
of PH |
[Arora] |
[Beame] [Spielman] |
[AB, Ch 5] [Pap, Sec16.2] |
[T,
Ch9] |
|
4 |
Jan
16 North 306 |
Space
Complexity: Savitch’s
proof PSPACE=NPSPACE L,
NL, Logspace Reductions |
[Arora] |
[Trevisan] |
[AB, Ch 3] [G, Ch5] [Pap, Ch19] |
[T,
Ch6] [T,
Ch10] [HMU,
Ch11] |
|
5 |
Jan
19 North 306 |
Space
Complexity, Cont: PSPACE
Complete Problems:Quantified Boolean Logic Complexity
of 2 Player Games Optional: Reingold's
deterministic logspace algorithm for undirected connectivity |
|
Optional: [Spielman] [Trevisan] [Trevisan] |
[G, Ch5] [Pap, Ch7,16] |
||
6 |
Jan
21 North 306 |
Diagonalization Time-Space
Hierarchy Theorems Oracle
Turing Machines |
[Arora] |
[Beame] |
[AB, Ch 4] [G, Ch4][Pap, Ch7,8][Pap, Ch14] |
|
|
7 |
Jan
28 North 306 |
Relativized
Proof Techniques Oracle
Turing Machines |
|
|
|
|
|
8 |
Feb
4 North 306 |
Kolmogorov
Complexity Definitions Incompressibility
for lowerbounds |
[Li] [Li] [Li] [Li] |
|
|
|
|
9 |
Feb
9 North 314 |
Overview
of Formal Recursion Theory and Automata |
|
|
|
|
|
10 |
Feb
11 North 306 |
Review
of Classical Complexity |
|
|
|||
|
Feb
13 North 306 |
Quiz
on Classical Complexity: -Speedup
& Slowdown Thms -Complexity
Classes -Reductions -Diagonalization |
|
|
|
|
|
11 |
Feb
18 North 306 |
Circuit
Complexity: Can
P/poly resolve P versus NP? P-Completeness
and Linear Programming Log-depth
Circuits, NC Examples
of NC parallel algorithms |
[Arora] |
[Beame] [Spielman] [Spielman] [Trevisan] |
[AB, Ch 6] [G, Ch3] [Pap, Ch11] |
|
|
12 |
Feb
20 North 306 |
Circuit
Complexity, Cont: Circuit
Lowerbounds: Parity
is not in AC0 proof with polynomials Hastad ‘s proof using
switching lemma Applications to learning Lowerbounds
for monotone circuits |
[Arora] |
[Arora] [Beame] [Beame] [Trevisan] [Trevisan] [Trevisan] |
[G, AppB] [Pap, Ch11] |
|
|
13 |
Feb
25 North
306 |
Quantum Computation Qubits Unitary Operations & Projections Quantum Circuits Example Quantum Computations |
[Arora] |
[Spielman] [Spielman] [Spielman] [Spielman] |
|
|
|
14 |
March
4 North 306 |
Quantum
Computation, Cont Qunatum Factoring Quantum Search Quantum Information Theory Quantum Compression |
[Arora] |
Shor’s Quantum
Algorithm for integer factorization [Spielman] Grover's Quantum
Algorithm for NP Search [Spielman] |
|
|
|
15 |
March
6 North 306 |
Randomized
Complexity: RP,
BPP, ZPP Proof
of the Schwartz-Zippel Lemma Error amplification Relation
of BPP to PH and P/poly |
[Arora] |
[Beame] [Spielman] |
[AB, Ch 7] [G, Ch6] |
[HMU,
Ch11] [G, AppD] |
|
|
March
7-15 |
No
Class - SPRING BREAK |
|
|
|
|
|
|
March
18* North
306 |
Mid-Term Exam |
|
|
|
|
|
16 |
March
20 North
306 |
Randomized Complexity, Cont: Probabilistic decision trees: Yao's lemma on decision trees Unique
Sat: The Valiant-Vazirani Theorem |
[Arora] [Spielman] [Trevisan] |
|
[G, Ch6] |
[HMU, Ch11] [G, AppD] |
|
17 |
March
25 North
306 |
Counting
Complexity Classes: #P
defined Permanent
is #P complete |
[Arora] [Beame] [Spielman] |
[Spielman] [Trevisan] |
[AB, Ch 7] [G, Ch6] |
|
|
18 |
March
27 North
306 |
Hardness
amplification and error correcting codes: Worst-case
to average case reduction. List
decoding and its use for hardness amplification |
[Arora] [Arora] |
|
[G, Ch7] [G, AppE] |
|
|
19 |
March
30 North
314 |
Recitation: Overview
of Cryptography: Trapdoor
Functions, Cryptography |
|
|
[Pap,
Ch18] [G, AppC] |
|
|
20 |
April
1 North
306 |
Pseudorandom
Number Generation: One
Way Functions: Discrete Log Goldreich-Levin
Hardcore Bit |
[Trevisan] |
|
[G, Ch8] [Pap,
Ch11] |
[G, AppC] |
|
21 |
April
3 North
306 |
Interactive Proofs (IP): -Interactive
proofs of graph non-isomorphism -Author-Merlin
Games Proof IP = PSPACE |
[Arora] |
[Beame] [Beame] [Beame] [Spielman] [Spielman] [Spielman] |
[AB, Ch 9] [G, Ch9] [Pap,
Ch19] |
|
|
22 |
April
6 North
314 |
Recitation: Introduction to Communication complexity |
[Arora] |
|
[AB, Ch 12] |
|
|
|
North
306 |
Hardness of Approximation: Overview of Direct Proof of PCP Theorem: NP in PCP(poly(n),1) |
[Beame] [Beame] [Beame] [Beame] |
[Spielman] [Spielman] [Spielman] [Spielman] |
|
|
|
|
North
306 |
Logic
& Proof in complexity theory: Why are
complexity lower bounds so difficult? Natural
proofs Proof
complexity Independence
in Logics |
[Arora] |
|
|
||
25 |
April
13 North
314 |
Recitation: Review
of Course Materials |
|
|
|
|
|
|
April
15 North
306 |
(FINAL
PROJECTS DUE in CLASS APRIL 15) Final
Exam -No
computers allowed -Open
book |
|
|
|
|
|
Required Class
Text Books: (digital text
books [AB] and [G] used by permission)
Additional Readings in Complexity
Theory: ([Tompa]
used by permission)
Lecture Notes
Credits: (all used by permission)