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lect01 - 6.841 Advanced Complexity Theory Feb 4, 2009...

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Unformatted text preview: 6.841 Advanced Complexity Theory Feb 4, 2009 Lecture 1 Lecturer: Madhu Sudan Scribe: Mergen Nachin 1 Administrative Information Lecturer: Madhu Sudan (madhu@mit.edu) TA: Brenden Juba (bjuba@mit.edu) Website: http://courses.csail.mit.edu/6.841/ The grading will be based on the following. Scribing - You must scribe at least one lecture no matter if you are taking the class for credit or as a listener. Problem sets - There will be roughly 3 problem sets throughout the semester. Participation - We encourage people to speak up, discuss and ask questions during the lecture. Project - Read papers about some topic and present it to the class (with additional progress, if possible). 2 High level overview of Computational Complexity Computational Complexity is concerned with the study of Interesting computational problems. Interesting resources such as time, space and etc. The feasibility and infeasibility - That is to prove upper and lower bounds. Unfortunately, we have a very few results on lower bounds for time or space. But on the other hand, we have made quite a progress on comparison lower bounds. For example, we compare two problems and conclude the following: if problem A requires some certain amount of resource to solve, then we must need at least some amount of resource to solve problem B. How do we define interesting? This is a very subjective choice. For example, a problem might be interesting if it has a lot of applications in a real world, or if many other problems can be reduced to one of its instances. Once we find an interesting problem, we want to find out how much time and space suffice to solve the problem, and how much are necessary to solve the problem. 2.1 Examples of interesting problems The following three problems are presented as interesting. #SAT (number-SAT): Given a 3CNF formula on n variables x 1 ,...,x n with m clauses c 1 ,...,c m (so = c 1 ... c m and each c i looks something like x i 1 x i 2 x i 3 ), count the number of satisfying assignments....
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This note was uploaded on 04/02/2010 for the course CS 6.841 taught by Professor Madhusudan during the Spring '09 term at MIT.

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lect01 - 6.841 Advanced Complexity Theory Feb 4, 2009...

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