Thanks everyone for your contributions to the class!


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...] 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...] Since I badly messed up the reduction from SUBSETSUM 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...] 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 1018, 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...] 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: www.liskovatuva.com. 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 Thursday, 1 April, Chemistry Auditorium, 2:00pm
Barbara Liskov, MIT 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). Here are links to some of the papers from today’s class:
Daniel raised the question last class about whether there is a nonrecursive 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 nonrecursive 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...] Here are the notes on regular languages. 

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