Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 6: Hardness via dictator vs. quasirandom tests
Feb. 1, 2007
Lecturer: Ryan ODonnell
Scribe: Amitabh Basu
In this lecture we show that constraint satisfaction is a hard problem. In particular
Analysis of Boolean Functions
CMU 18-859S, Spring 2007
P ROBLEM S ET 1
Due: Thursday, February 1
Homework policy: I encourage you to try to solve the problems by yourself. However, you may
collaborate as long as you do the writeup yourself and list the pe
Analysis of Boolean Functions
CMU 18-859S, Spring 2007
P ROBLEM S ET 2
Due: Tuesday, February 20
Homework policy: I encourage you to try to solve the problems by yourself. However, you may collaborate
as long as you do the writeup yourself and list the pe
Analysis of Boolean Functions
CMU 18-859S, Spring 2007
P ROBLEM S ET 3
Due: Thursday, March 8
Homework policy: I encourage you to try to solve the problems by yourself. However, you may collaborate
as long as you do the writeup yourself and list the peopl
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 9: Learning Decision Trees and DNFs
Feb. 18, 2007
Lecturer: Ryan ODonnell
Scribe: Suresh Purini
1 Two Important Learning Algorithms
We recall the following denition and two important learnin
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 12: Social Choice, Condorcet, and Majority
Feb. 22, 2005
Lecturer: Ryan ODonnell
1
Scribe: Aaron Roth
Social Choice Theory
Social choice theory studies the aggregation of many individual pre
Almost Linear Functions
-Afunctionf:Fn2F2islinearifeitherofthefollowingequivalentconditionshold:
f(x+y)=f(x)+f(y)forallx,yFn2;
f(x)=axforsomeaFn2;i.e.,f(x)=iSxiforsomeS[n].
Ifweencodetheoutputoffby1Rintheusualwaythenthelinearfunctionsf:Fn2 cfw_1,1
areprec
DecisionTree
Adecisiontreeisadecisionsupporttoolthatusesatreelikegraphormodelofdecisions
and their possible consequences, including chance event outcomes, resource costs, and
utility.
Adecisiontreeconsistsof3typesofnodes:
Decisionnodescommonlyrepresentedb
Analysis of Boolean Functions
CMU 18-859S, Spring 2007
P ROBLEM S ET 4
Due: Tuesday, April 3, beginning of class
Homework policy: I encourage you to try to solve the problems by yourself. However, you may collaborate
as long as you do the writeup yourself
Analysis of Boolean Functions
CMU 18-859S, Spring 2007
P ROBLEM S ET 5
Due: Tuesday, April 24, beginning of class
Homework policy: I encourage you to try to solve the problems by yourself. However, you may collaborate
as long as you do the writeup yoursel
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 7: The Goldreich-Levin Algorithm
Feb. 6, 2007
Lecturer: Ryan ODonnell
Scribe: Karl Wimmer
In this lecture we make the jump from testing properties of functions to learning functions.
The rst
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 8: Learning under the uniform distribution
Feb. 8, 2005
Lecturer: Ryan ODonnell
1
Scribe: Moritz Hardt
The Learning Model
A learning problem is identied with a (concept) class C of functions
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 10: Learning DNF, AC0, Juntas
Feb 15, 2007
Lecturer: Ryan ODonnell
Scribe: Elaine Shi
1 Learning DNF in Almost Polynomial Time
From previous lectures, we have learned that if a function f is
Analysis of Boolean Functions
CMU 18-859S / 21-801A, Fall 2012
Problem Set 1
Due: Monday, Sept. 17, beginning of class
Homework policy: Please work on the homework by yourself; it isnt intended to be too dicult.
Questions about the homework or other cours
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 11: Learning juntas with Siegenthalers Theorem
Feb. 20, 2007
Lecturer: Ryan ODonnell
Scribe: Yi Wu
1 The problem of learning r-junta
Problem: Let Cr = cfw_f : cfw_1, 1n and f is r-junta, we
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 5: Introduction to Hardness of Approximation
Jan. 30, 2007
Lecturer: Ryan ODonnell
Scribe: Eric Blais
In this lecture, we introduce some of the tools that will enable us to prove strong stat
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 4: Locally testing Dictatorship with NAE; explicit PCPPs
Jan. 25, 2005
Lecturer: Ryan ODonnell
1
Scribe: Aaron Roth
A Local Test for Dictatorship
The Marquis de Condorcet was a French mathem
Analysis of Boolean Functions
CMU 18-859S / 21-801A, Fall 2012
P ROBLEM S ET 2
Due: Monday, Sept. 24, beginning of class
Turn in problems #1#4, plus either #5 or #6
Homework policy: Please work on the homework by yourself; it isnt intended to be too difcu
Analysis of Boolean Functions
CMU 18-859S / 21-801A, Fall 2012
P ROBLEM S ET 6
Due: Wednesday, Oct. 24, beginning of class
Homework policy: Questions about the homework or other course material can be asked on Piazza.
R
R
1. Let A cfw_1, 1n have cardinali
Analysis of Boolean Functions
CMU 18-859S / 21-801A, Fall 2012
P ROBLEM S ET 4
Due: Monday, Oct. 8, beginning of class
Homework policy: Please try to work on the homework by yourself; it isnt intended to be too
difcult. Questions about the homework or oth
Analysis of Boolean Functions
CMU 18-859S / 21-801A, Fall 2012
P ROBLEM S ET 5
Due: Monday, Oct. 15, beginning of class
Homework policy: Please try to work on the homework by yourself; it isnt intended to be too
difcult. Questions about the homework or ot
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 3: The BLR and Hstad Tests; local testing and decoding
Jan. 23, 2005
Lecturer: Ryan ODonnell
1
Scribe: Samid Hoda
Proof of the BLR Test
As promised we will nish the proof of the BLR test tha
Analysis of Boolean Functions
(CMU 18-859S, Spring 2007)
Lecture 2: Linearity and the Fourier Expansion
Jan. 18, 2005
Lecturer: Ryan ODonnell
1
Scribe: Ryan ODonnell
Linearity
What does it mean for a boolean function to be linear? For the question to make