CSE540 Theory of Computation (Fall 2016)
In a nutshell, this course is about “sequencing the DNA of computation”. You will see a lot of fancy stuff that you do not get to see elsewhere, and you should be prepared for some hard work. Students who are motivated to understand the theoretical foundations of computation, have a solid math background, and enjoy reading and writing rigorous mathematical arguments are particularly encouraged to take this course.
More specifically, the purpose of the course is to study the capabilities and limitations of computers by formulating mathematically various models of idealized computers and establishing rigorously for these models what kinds of problems can and cannot be solved, as well as what kinds of problems can and cannot be solved with a reasonable amount of computing resources.
Topics include but not limited to:
Computability theory: Turing machines, Church-Turing thesis, halting problem and undecidability, universal Turing machine, introductory recursion theory;
Complexity theory: complexity measures, time and space hierarchy, NP-complete problems, intractability;
Advanced topics: probabilistic algorithms, interactive proofs, cryptography, computational game theory. Exact topics covered depend on the class progress.
An introductory treatment of Turing machines would typically be part of an undergraduate course in the theory of computation, which is a prerequisite for this course. Though I will cover this topic, the treatment will be fairly speedy, so as to leave enough time for other topics.
Instructor: Jing Chen
Office: 247 Computer Science
Fall 2016 Office Hour: Monday 4:00-5:00pm or by appointment
Prerequisite: CSE303 or equivalent ones
Lecture: MW 2:30-3:50pm, Room 2120, old CS building
Textbook: Introduction to the Theory of Computation, M. Sipser, 3rd edition.
Recommended reading: Computational Complexity, S. Arora and B. Barak.
Course website: http://www3.cs.stonybrook.edu/~cse540/
· We will use Blackboard (http://blackboard.stonybrook.edu/) for future announcements and course materials. Course Calendar can be found in Course Tools.
· Syllabus from 2015. Materials covered this year may be adjusted.
· Please type your homework solutions using LaTeX. Template is here.
· Problem Set 0: Academic Honesty Review. Due in class by Sep. 7, 2:30pm.
The grade will be based on the following parts.
· Homework (20 points in total)
Homework assignments will be bi-weekly or tri-weekly. You can discuss the problems with other students taking this class, and actually you are encouraged to do so. But I suggest you not discuss a problem with others until you have made serious effort trying to solve it by yourself.
You must write up and submit your solution individually, and you must acknowledge for each problem with whom you have discussed. If more than one student submits substantially the same writeup for a particular problem, or if there is some other evidence that the writeup you submit is not your own work, I will regard this as evidence that you are trying to get a higher grade without actually doing the required work and may choose either to make a corresponding deduction from your homework score or (in egregious cases) to pursue the matter as a case of academic dishonesty.
Note! If you really don’t know how to solve a problem after making serious effort, write “I honestly don’t know how to solve this problem” and you’ll get 25% of it. While if you “make up” a solution by putting together some random sentences, you may get lower than that. Indeed, to realize that you don’t understand something is an important step towards understanding it.
· Two in-class exams (60 points in total)
· Course project (15 pts)
You’ll form groups (group size depending on class size). Each group will choose 1 paper and present to the class. The paper must be published in the last 5 years in major theory conferences and the topic must be related to the materials covered in class.
· Class participation (5 pts)
I encourage you to answer questions and to ask questions in class, as interaction is an efficient way of learning.
· Bonus (5 pts)
For homework and exam problems, I may need students to prepare detailed solutions to be distributed to the class. You can claim the 5 bonus points by preparing solutions for problems that I assign to you.
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