6.080/6.089 GITCS
May 13, 2008
Lecture 24
Lecturer: Scott Aaronson
1
Scribe: Chris Granade
Quantum Algorithms
Of course the real question is: can quantum computers actually do something more eciently than
classical computers? In this lecture, well see why
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 10
Nancy Lynch
Today
Final topic in computability theory: Self-Reference
and the Recursion Theorem
Consider adding to TMs (or programs) a n
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 9
Nancy Lynch
Today
Mapping reducibility and Rices Theorem
Weve seen several undecidability proofs.
Today well extract some of the key ide
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 8
Nancy Lynch
Today
More undecidable problems:
About Turing machines: Emptiness, etc.
About other things: Post Correspondence Problem.
To
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 7
Nancy Lynch
Today
Basic computability theory
Topics:
Decidable and recognizable languages
Recursively enumerable languages
Turing Machine
6.080/6.089 GITCS
Feb 14, 2008
Lecture 4
Lecturer: Scott Aaronson
1
Scribe: Aseem Kishore
Previously in 6.089.
Last lecture, we talked about two dierent models of computation, nite automata and circuits.
Finite automata allowed us to recognize many proper
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 5
Nancy Lynch
Today
Non-regular languages
Todays topics:
Existence of non-regular languages
Showing some specific languages arent regular
T
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 4
Nancy Lynch
Today
Two more models of computation:
Nondeterministic Finite Automata (NFAs)
Add a guessing capability to FAs.
But
6.045: Automata, Computability, and
Complexity
Or, Great Ideas in Theoretical
Computer Science
Spring, 2010
Class 3
Nancy Lynch
Today
Finite Automata (FAs)
Our third machine model, after circuits and decision trees.
Designed to:
Accept some strings of
6.080/6.089 GITCS
Feb 12, 2008
Lecture 3
Lecturer: Scott Aaronson
1
1.1
Scribe: Adam Rogal
Administrivia
Scribe notes
The purpose of scribe notes is to transcribe our lectures. Although I have formal notes of my own,
these notes are intended to incorporat
6.080/6.089 GITCS
April 8, 2008
Lecture 15
Lecturer: Scott Aaronson
1
Scribe: Tiany Wang
Administrivia
Midterms have been graded and the class average was 67. Grades will be normalized so that the
average roughly corresponds to a B. The solutions will be
6.045: Automata, Computability, and
Complexity
Or, GITCS
Class 12
Nancy Lynch
Today: Complexity Theory
First part of the course: Basic models of computation
Circuits, decision trees
DFAs, NFAs:
Restricted notion of computation: no auxiliary memory, ju
6.080/6.089 GITCS
April 4th, 2008
Lecture 16
Lecturer: Scott Aaronson
Scribe: Jason Furtado
Private-Key Cryptography
1
Recap
1.1
Derandomization
In the last six years, there have been some spectacular discoveries of deterministic algorithms,
for problems
6.080/6.089 GITCS
May 6-8, 2008
Lecture 22/23
Lecturer: Scott Aaronson
1
1.1
Scribe: Chris Granade
Quantum Mechanics
Quantum states of n qubits
If you have an object that can be in two perfectly distinguishable states |0 or |1, then it can also
be in a su
6.080/6.089 GITCS
Feb 5, 2008
Lecture 21
Lecturer: Scott Aaronson
1
Scribe: Scott Aaronson / Chris Granade
Recap and Discussion of Previous Lecture
Theorem 1 (Valiant) m = O
1
log (|C | / ) samples suce for (, )-learning.
Theorem 2 (Blumer et al.) m = O
1
6.080/6.089 GITCS
1 April 2008
Lecture 20
Lecturer: Scott Aaronson
Scribe: Georey Thomas
Probably Approximately Correct Learning
In the last lecture, we covered Valiants model of Probably Approximately Correct (PAC) learn
ing. This involves:
S:
A sample s
6.080/6.089 GITCS
April 24, 2008
Lecture 19
Lecturer: Scott Aaronson
1
Scribe: Michael Fitzgerald
Recap And Discussion Of Previous Lecture
In the previous lecture, we discussed dierent cryptographic protocols. People asked: In the RSA
cryptosystem, why do
6.080/6.089 GITCS
April 17, 2008
Lecture 18
Lecturer: Scott Aaronson
1
Scribe: Hristo Paskov
Recap
Last time we talked about public key cryptography which falls in the realm of accomplishing bizarre
social goals using number theory. Our rst example of a p
6.045: Automata, Computability, and
Complexity (GITCS)
Class 17
Nancy Lynch
Today
Probabilistic Turing Machines and Probabilistic
Time Complexity Classes
Now add a new capability to standard TMs:
random choice of moves.
Gives rise to new complexity cla
6.045: Automata, Computability, and
Complexity (GITCS)
Class 16
Nancy Lynch
Today: More NP-Completeness
Topics:
3SAT is NP-complete
Clique and VertexCover are NP-complete
More examples, overview
Hamiltonian path and Hamiltonian circuit
Traveling Salesman
6.045: Automata, Computability, and
Complexity (GITCS)
Class 15
Nancy Lynch
Today: More Complexity Theory
Polynomial-time reducibility, NP-completeness,
and the Satisfiability (SAT) problem
Topics:
Introduction (Review and preview)
Polynomial-time reduc
6.080/6.089 GITCS
Apr 15, 2008
Lecture 17
Lecturer: Scott Aaronson
1
Scribe: Adam Rogal
Recap
1.1
Pseudorandom Generators
We will begin with a recap of pseudorandom generators (PRGs). As we discussed before a
pseudorandom generator is a function that take
6.080/6.089 GITCS
Feb 5, 2008
Lecture 1
Lecturer: Scott Aaronson
1
Scribe: Yinmeng Zhang
Administrivia
Welcome to Great Ideas in Theoretical Computer Science. Please refer to the syllabus for course
information.
The only prerequisite for the class is math