{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lect01

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

This preview shows pages 1–2. Sign up to view the full content.

6.841 Advanced Complexity Theory Feb 4, 2009 Lecture 1 Lecturer: Madhu Sudan Scribe: Mergen Nachin 1 Administrative Information Lecturer: Madhu Sudan ([email protected]) TA: Brenden Juba ([email protected]) 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 φ on n variables x 1 , . . . , x n with m clauses c 1 , . . . , c m (so φ = 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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online