Class 28: Cakes and Theory in Jeopardy!

Class 28 slides: [PPTX] [PDF]

Jeopardy slides: [PPTX] [PDF]

Thanks everyone for your contributions to the class!

Factorial is faster than Exponential!

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 [More...]

Class 27: NP-Complete Desserts

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 [More...]

Class 26: NP-Complete Entrees

Class 26 slides: [PPTX] [PDF]

Class 25: NP-Complete Appetizers

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, [More...]

Class 24: NP-Completeness

Class 24 slides: [PPTX] [PDF]

Class 23: P = NP?

Class 23 slides: [PPTX] [PDF]

Class 22: Introducing Complexity

Class 22 slides: [PPTX] [PDF]

Class 21: Undecidability in Theory and Practice

Class 21 slides: [PPTX] [PDF]

Class 20: Busy Beavers

Class 20 slides: [PPTX] [PDF]

Tuesday's Class, Preparing for Exam 2

Exam 2 will be handed out Thursday, April 8 and due Tuesday, April 13. It will cover everything through today’s class (Barbara Liskov’s lecture), but emphasize things that have been covered since Exam 1: class 10-18, Problem sets 4 and 5.

If you have any topics you would like me to review in class Tuesday, or questions you want me to go over, please post them here.

As a separate game theory challenge, if exactly ONE student in [More...]

Thursday’s Class: Barbara Liskov’s Talk

Remember that Thursday’s class will be Barbara Liskov’s talk in Chemistry Auditorium. This is at the same time (2:00pm) as our class normally meets.

Everyone should find Prof. Liskov’s talk interesting and exciting. You can read more about the talk and her background here:

Class 18: Proving Undecidability

Class 18 slides: [PDF] [PPTX]

Sorry to be so rushed for the last part of class today. We’ll spend more time in next Tuesday’s class on undecidable and decidable properties of programming languages.

Upcoming Turing Award Winner Talks

Next week there will be two Turing award winners visiting UVa and giving public talks.

Monday, 29 March, MEC 205 (CHANGE IN VENUE), 3:30pm

Edmund Clarke, Carnegie Mellon University
Model Checking: My 27 year Quest to Overcome the State Explosion Problem

Thursday, 1 April, Chemistry Auditorium, 2:00pm

Barbara Liskov, MIT
Security of Internet Storage

Note that Thursday’s talk is during our scheduled class time. Students should attend Prof. Liskov’s talk (and expect to have questions on the exam based on her talk).

Class 17: Undecidable Languages

Class 17 slides: [PPTX] [PDF]

Class 15: Church-Turing Thesis

Class 15: [PPTX] [PDF]

Class 14: Turing Machines

Class 14 slides: [PDF] [PPTX]

Class 11: Moore, Mealy, and Markov

Class 11 slides: [PDF] [PPTX]

Here are links to some of the papers from today’s class:

Class 10

Class 10 slides: [PPTX] [PDF]

If you have topics or questions you want me to review in Thursday’s class, post comments here.

Class 9: Context-Free Languages Contextually

Class 9 slides: [PPTX] [PDF]

Class 8: Non-Context-Free Languages

Class 8 slides: [PPTX] [PDF]

Non-Recursive Human Languages?

Daniel raised the question last class about whether there is a non-recursive human language. Although I felt quite confident in class that such a thing could not exist, there have been some controversial claims about the existence of a non-recursive human language. The language in question is known as Pirahã, spoken by a remote tribe in the Brazillian Amazon. Dan Everett, now a professor of Linguistics at Illinois State University, studied the Pirahã language [More...]

Class 7: Context-Free Languages

Class 7 slides: [PPTX] [PDF]

(My tablet has a bad habit of crashing between the classroom and my office, so I lost the ink for this class. I’ve tried to recreate the most important ink on the slides.)

Class 6: Deterministic Pushdown Automata

Class 6 slides: [PDF] [PPTX]

Notes on PDAs

Class 5: Non-Regular Languages

Here are the notes on regular languages.

Class 5 slides: [PPTX] [PDF]