CSE 200 Computability and Complexity
Monday, April 15, 2013
Lecture 5: NP-Completeness (cont.)
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
Recap
Lets review NPs denition taught in the last class.
NP = Problems whose solution can be veried
CSE 200 Computability and Complexity
Wednesday, April 17, 2013
Lecture 6: Polynomial Hierarchy
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
2-SAT
Theorem 1 2-SAT P.
Proof Suppose we have a 2-CNF formula (x1 x2 ) (x2 x3 ) (x4 x6 ) . The algo
CSE 200 Computability and Complexity
Monday, April 8, 2013
Lecture 3: Time Complexity & Space Complexity
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
Intriguing Problems
Matrix Multiplication. Given two n n matrices. A trivial algorithm use
CSE200: Computability and complexity
Homework set 2 solution
Shachar Lovett
1
Primality in NP
To prove that a number n is prime, the proof is composed of:
r
i=1 qi .
1. Numbers q1 , . . . , qr such that n 1 =
2. Number a cfw_2, 3, . . . , n 1 such that an
CSE200: Computability and complexity
Homework set 1 solution
Shachar Lovett
1
Single tape Turing machine
We need to prove that the standard 3-tape Turing machine (with separate tapes for input,
work and output) can be simulated by a single Turing machine.
CSE200: Computability and complexity
Homework set 3
Shachar Lovett
Due by May 29 (hand in class)
1
Schning algorithm for 3SAT
o
We will analyze Schnings randomized algorithm for 3SAT [Sch99]. Let us recall the
o
algorithm. Let (x1 , . . . , xn ) = C1 (x)
CSE 200 Computability and Complexity
Wednesday, April 3, 2013
Lecture 2: Uncomputability and the Haling Problem
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
The Universal Turing Machine
In the last class, we saw that the denition of TM is r
CSE 200 Computability and Complexity
Monday, May 6, 2013
Lecture 11: Circuit Lower Bounds
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
Circuit Classes: NCi and ACi
There are specic kinds of circuits for which lower bounds techniques were su
CSE 200 Computability and Complexity
Monday, May 20, 2013
Lecture 15: Randomized Computation (cont.)
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
Random Walk Algorithms for k-SAT
1.1
A random walk algorithm for 2-SAT
2-SAT. (x) = (x1 x2 ) (
CSE 200 Computability and Complexity
Monday, May 13, 2013
Lecture 13: Randomized Computation
Instructor: Professor Shachar Lovett
1
1.1
Scribe: Dongcai Shen
Randomized Complexity
Randomness is powerful
We are interested in knowing: to what extent does ran
CSE 200 Computability and Complexity
Wednesday, May 1, 2013
Lecture 10: Boolean Circuits (cont.)
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
Recap
Denition 1 (Boolean circuit) A Boolean circuit on n inputs, is a DAG with n source nodes and
CSE 200 Computability and Complexity
Monday, April 22, 2013
Lecture 7: Space Complexity
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
LOGSPACE Reduction L
This week we will talk about space complexity. We started at poly-time (P) to investig
CSE 200 Computability and Complexity
Wednesday, April 24, 2013
Lecture 8: PSPACE-Completeness & Savitchs Theorem
Instructor: Professor Shachar Lovett
1
Scribe: Dongcai Shen
Recap: Space Complexity
Recall the following denitions on space complexity we lear
CSE200: Computability and complexity
Homework set 2
Shachar Lovett
Due by May 13th (hand in class)
1
Primality in NP
Let PRIMES be set of prime numbers. It is easy to see that P RIM ES coN P since
a certicate for non-primality (e.g. for being composite) o
CSE200: Computability and complexity
Final Exam
Shachar Lovett
Due by June 14th
The nal take-home exam is individual. You are not allowed to consult with any other
students or any other person for that matter, except for the professor or the TA. Cite any
CSE200: Computability and complexity
Homework set 1
Shachar Lovett
Due by April 24 (hand in class)
1
Single tape Turing machine
Consider the following model of a Turing machine: a Turing machine with a single read/write
tape, used both for input, work and
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
Problem Set 6 Solutions
Winter 11
Instructor: Mihir Bellare
March 9, 2011
Problem Set 6 Solutions
In all problems the languages are over the alphabet = cfw_0, 1. If x, y are stri
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
Problem Set 5 Solutions
Winter 11
Instructor: Mihir Bellare
February 23, 2011
Problem Set 5 Solutions
In all problems the languages are over the alphabet = cfw_0, 1. You may use
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
Notes on Randomized Algorithms
Winter 10
Instructor: Mihir Bellare
January 3, 2010
Notes on Randomized Algorithms
Randomness can help to solve problems and is a fundamental ingre
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
Course Information
Winter 10
Instructor: Mihir Bellare
January 3, 2010
Course Information
Meets: M and W, 9:30AM10:50AM in EBU3B 2154.
Instructor: Mihir Bellare
Instructors Oce:
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
Decision versus Search
Winter 10
Instructor: Mihir Bellare
January 3, 2010
Decision versus Search
When we want to solve a problem in real life, we are interested in nding a solut
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
Computability Crib Sheet
Winter 10
Instructor: Mihir Bellare
January 3, 2010
Computability Crib Sheet
This is a quick reference sheet for the denitions, theorems and examples in
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
An example of a NP-completeness proof
Winter 11
Instructor: Mihir Bellare
January 3, 2011
An example of a NP-completeness proof
In class I stress the intuitive aspects of the red
Computer Science and Engineering, UCSD
CSE 200: Computability and Complexity
Problem Set 2
Winter 11
Instructor: Mihir Bellare
January 12, 2011
Problem Set 2
Due: Wednesday January 19, 2011, in class.
The Computability Crib Sheet, available from the cours