CS 521 Spring 2010

This course is now complete. We covered most of Chapters 1-5,7,9-10 of the Arora/Barak book. The material was covered by my introducing the first half of each chapter in one lecture and the students presenting the remainder over the next lecture or two. Presentations ran from 10-30 minutes long. Every student was responsible for presenting some topic from each chapter covered. The final essays explored topics not covered in the course and are available here:

Overview

This course will (hopefully) cover Chapters 1-3 and 7-11 of Computational Complexity by Arora and Barak. I am hoping to cover the material at a high/non-technical level to expose you to a broad range of topics. We will consider the following questions:

  • Why don't we have efficient algorithms for the problems we really need to solve?
  • Do random algorithms outperform deterministic algorithms?
  • Can we use computationally hard problems to devise cryptographic protocols?
  • What would be the consequences of building a quantum computer?

A large part of your grade will be determined by an essay on a topic in computational complexity of your choice?.

Schedule

width="50pt" | Week

Plan

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1

 Review: Turing machine models, P and computability.
Read: Chapter 1 of Arora/Barak
References:

Turing machines (Stanford Encyclopedia of Philosophy),
oblivious Turing machines (Lipton), sorting networks and randomized Shell sort (Goodrich)
Presentation assignments for April 1?

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2

 Read: Chapter 2 of AB
Presentation assignments for April 8?
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3

 Proposed essay topics due: Email a description of your topic and why you are interested in it. Include at least 3 references (at least one traditionally published reference).
I will give feedback on your topic as well as your general class participation as quickly as possible.
From Chapter 3, we covered just the statement of Ladner's Theorem.
Two proofs of Ladner's Theorem (Fortnow) and the Complexity Zoo
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4

 Read: Chapter 4
Presentation assignments for April 20?
The Polynomial Hierarchy (wikipedia) and it's collapse! (Scott Aaronson)
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5

 Tuesday's class is cancelled.
Remember that you need to visit the Writing Center - it will be easier to get an appointment earlier in the quarter.
Read: Chapter 7
References: Polynomial identity testing and applications (Ronitt Rubinfeld)
6?
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6

 Essay draft due: see here? for formatting details.
ZPP = RP cap co-RP and more (Rave Harpaz)
Randomized reductions (Luca Trevisan)
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7

 Tuesday's class is cancelled.
20?
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8

 Peer reviews due: see here? for review guidelines.

Radiolab episode on randomness

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9

 2?
Quantum Superposition - cartoon description, Double slit experiment, Heisenberg's Uncertainty Principle, Quantum superposition of larger-scale objects (news article)
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10

 Final essay due

Essay-related due dates: are on Tuesday of the listed week. However, you may submit your material as late as Thursday. There are benefits to submitting your material as early as possible: quicker feedback, longer for your classmates to review your essay, etc. Extensions beyond Thursday will not be given except for reasons of health, extreme emergencies.

Evaluation

Your grade will be determined as follows:

Class participation, assignments, quizzes,
wiki participation, etc 		40% - Peer reviews 20%
Essay 40%

Assignments and quizzes will be informal and will likely be participatory. As such, I will aim to give projected grades for class participation, assignments and quizzes at weeks 3 and 7.