CSE4115, Fall 2012

Computational Complexity
Fall 2012

Web page contents:

General Information
Important Dates
Course Handouts

General Information

Instructor: Eric Ruppert
Office: Lassonde (Computer Science) Building, room 3042
Email: [my last name] @cse.yorku.ca
Telephone: (416) 736-2100 ext. 33979
Facsimile: (416) 736-5872
Lectures: Mondays and Wednesdays from 14:30 to 16:00 in room 122 of the Chemistry building.
Office Hours: I will hold regular office hours on Mondays from 12:00 to 1:00 and Wednesdays from 4:00 to 5:00. If you cannot make it at those times, feel free to contact me to make an appointment at a different time. You can also try dropping by my office.

The best way to contact me is probably by email. Please use your cs account when sending me email, and start your subject line with "[4115]". Send messages in plain text, without attachments.

Course Overview

This course is intended to introduce students to the fundamentals of complexity theory, which is an important part of the foundations of the entire field of computer science.

We'll look at models of computers (e.g. Turing machines) and see how they are used to measure the resources (time, space and others) required to solve problems. If we pick a model and a bound on one or more resources, we can define a complexity class (e.g. P, NP, NC) to be the set of problems that can be solved in that model with the given resources. These classes give us a systematic way of understanding how efficiently problems can be solved.

In studying complexity theory, we learn about techniques that can be used to design efficient algorithms. We also learn how to identify those problems for which efficient solutions do not exist or are unlikely to exist. Such information is useful, because it often suggests how to modify our approach when faced with an intractable problem: for example, we might look for approximate solutions instead of exact solutions, or try to solve a special case of the problem that is sufficient for our needs.

This course assumes knowledge of the material in CSE2001 and CSE3101, and you should be comfortable reading and writing mathematical proofs.

Here is a tentative list of topics:

Marking scheme

Homework exercises 30%
Midterm test 20%
Class presentation10%
Classroom participation10%
Final exam 30%

Academic Honesty

It is important that you look at the departmental guidelines on academic honesty.

Although you may discuss the general approach to solving a problem on a homework assignment with other people, you should not discuss the solution in detail. You must not take any written notes away from such a discussion. Also, you must list on the cover page of your solutions any people with whom you have discussed the problems. The solutions you hand in should be your own work. While writing them, you may look at the course textbook and your own lecture notes but no other outside sources.

If you get stuck while working on one of the assignments, I encourage you to come to my office hours to get help with it.


Important Dates

(Information will be added to this table thoughout the term.)

First class September 5
Thanksgiving (no lecture) October 8
Midterm test October 24
Hallowe'en (no lecture) October 31
Drop deadline November 9
Last class December 3
Exam period December 5-21


Course Textbook

[Sip] Michael Sipser. Introduction to the Theory of Computation, 3rd edition. Cengage Learning, 2013.
We will be focusing on Part III of the book.
If you have the 2nd edition, that's fine (there are not very many differences between the two editions).
The textbook website has lists of errata.

Other Books

Original Articles

Resources for Special Topics

More advanced complexity resources


DateSectionSuggested Exercises
Sep 5Review chapter 0 and 30.1-0.8, 3.1-3.2, 3.7, 3.8, 3.10-3.13
Sep 107.1, review 3.17.1, 7.2, 3.8
Sep 12notes suppliedShow every single-tape TM that decides {0x1y2x : x,y ≥ 0} takes Ω(n log n) steps
Sep 17review 3.2, supplementary reading: Sec 2.6 of [Pap]3.12, 3.13
Sep 197.27.3-7.6, 7.8, 7.9, 7.13, 7.14, 7.15
Sep 247.37.7, 7.12, 7.16
Sep 267.47.18, 7.20-7.27
Oct 1-227.5 and package of NP-completeness results handed out7.17, 7.28, 7.30-7.33, 7.35, 7.38, 7.40-7.41
Oct 298.0-8.1, 8.48.1, 8.4, 8.7, 8.9, 8.17, 8.20, 8.22
Nov 58.5, 8.68.25,8.29,8.32
Nov 149.19.1-9.3,9.12,9.13
Nov 199.3,10.5
Nov 218.2
NOTE: Exercise numbers are from the third edition of the textbook.

Course Handouts

Updated November 23, 2012