cs3102: Theory of Computation

Final Comments

evans — Sat, 15 May 2010 02:17:49 +0000

I have posted the final grades in SIS, so you should be able to see them soon (at least by tomorrow).

Comments on the final exam: [PDF]

Thanks everyone for a great semester, and enjoy your summer!

Conveying Complexity Highlights

evans — Sat, 15 May 2010 02:16:52 +0000

This page: Conveying Complexity Highlights contains links to some of the most interesting, illuminating, and/or entertaining submissions for PS7. Enjoy watching the movies, listening to the music, and playing the games! (Alas, HTTP 1.1 does not provide any support for transmitting cakes, however.)

Final Exam Information

evans — Tue, 04 May 2010 20:27:32 +0000

The final exam is Thursday, May 13, 9am-noon (as scheduled by the registrar).

It covers the whole course:

(in theory) anything in Problem Sets 1-7, Exams 1-2, Classes 1-28, Sipser Ch 1-5+7, Liskov’s talk, assigned readings
(in practice) emphasizes most important things that have been covered many times; slight emphasis on material since Exam 2

It will be similar to Exams 1 and 2 except that no resources may be used (no notes at all!).

I will be out of town Thursday and Friday so will not hold office hours this Thursday. Next week there will be two scheduled office hours:

Office Hours, Monday (10 May) 1:30-3pm
Office Hours, Wednesday (12 May) 4-5:30pm

I am willing to entertain any questions you want during these times, but may decide not to some answer questions directly related to the exam preview handout [PDF].

Class 28: Cakes and Theory in Jeopardy!

evans — Tue, 04 May 2010 20:20:01 +0000

Class 28 slides: [PPTX] [PDF]

Jeopardy slides: [PPTX] [PDF]

Thanks everyone for your contributions to the class!

Factorial grows faster than Exponential!

evans — Tue, 04 May 2010 20:05:30 +0000

Sorry, I was wrong for one of the Jeopardy answers today!

n! is not in O(2ⁿ).

It is easy to see that n! < nⁿ, since all the numbers in the product to compute n! are less than (or equal to) n, but this doesn’t prove it is not in O(2ⁿ). For that, we can use Sterling’s approximation which gives a tight approximation of the value of n! as

which is definitely not in O(2ⁿ) since the base of the exponent is not a constant.

For details, see this wikipedia page.

Sorry I was confused on this today! I was thinking of Fibonacci, which is approximated by φⁿ where φ is the golden ratio (1.618…). This is in O(2ⁿ) since 1.618… < 2.

I hope it didn’t change the outcome of the game. As my penance, maybe I should add a question related to this on the final to redeem myself.

PS7 Submissions

evans — Mon, 03 May 2010 15:01:00 +0000

Please submit your PS7 by posting a comment to this post.

Some reminders from the PS7 handout are below, see that handout for full details.

If you work in a team, your team should jointly post a single submission with all of your names on it.

Your post should include:

the names of everyone on the team
a description of your target audience
either the artifact itself or a link to it if it is hosted elsewhere
(optionally) a poetic license statement

Note: if you log into your account on this blog, you can post a comment without needing moderation. Otherwise, you can post a comment but it won’t appear until I approve it.

Remember to send me email before 5pm today (Monday, May 3) if you would like to present or perform your artifact in class tomorrow.

Class 27: NP-Complete Desserts

evans — Thu, 29 Apr 2010 23:53:32 +0000

Class 27 slides: [PPTX] [PDF]

In class, someone asked about languages known to be in BQP that are not known to be in NP. There is at least one such language, known as the Recursive Fourier Sampling problem. It is described in this paper: Quantum complexity theory by Ethan Bernstein and Umesh Vazirani, ACM Symposium on Theory of Computing, 1993. [Full version: PDF] Section 8.4 of this paper describes the problem, but it is definitely not light reading! Before tackling this paper, I would recommend reading Scott Aaronson’s Scientific American article: The Limits of Quantum Computers.

Grades in Collab

evans — Thu, 29 Apr 2010 15:49:59 +0000

I have uploaded your scores on assignments into Collab so you can now verify that I have all your scores recorded correctly. If you notice any discrepancies, please let me know.

Class 26: NP-Complete Entrees

evans — Tue, 27 Apr 2010 20:01:19 +0000

Class 26 slides: [PPTX] [PDF]

Class 25: NP-Complete Appetizers

evans — Thu, 22 Apr 2010 19:47:00 +0000

Class 25 slides: [PPTX] [PDF]

Since I badly messed up the reduction from SUBSET-SUM to KNAPSACK, and don’t see an obvious way to fix this, you can solve this question in place of Problem 5 on PS6. If you get an especially elegant and convincing answer that you would like to present in class Tuesday, send it to me by Monday afternoon.

The reading handed out today is available here: The Status of the P versus NP Problem, Lance Fortnow, Communications of the ACM, September 2009.