EECS 4115/5115, Fall 2020
EECS 4115/5115
Computational Complexity
Fall 2020
Web page contents:
General Information
Announcements
Important Dates
Resources
Reading
Course Handouts
General Information
Instructor: Eric Ruppert
Email: [my last name] @eecs.yorku.ca
Lectures: Tuesdays and Thursdays from 11:30 to 13:00 via Zoom meetings. See course eclass page for meeting details.
Office Hours: Mondays at 2pm and Thursdays at 3pm via Zoom meetings. See course eclass page for meeting details.
When emailing, please use your cs account when sending me email, and start your subject line with "[4115]" for faster attention.
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:
- Models of computation: various types of Turing Machines, Random Access Machines
- Definitions of some basic complexity classes (LOGSPACE, P, NP, coNP, PSPACE) & relationships between them
- Time & space hierarchy theorems
- Reductions, NP-completeness
- Parallel computation (circuits, Parallel Random Access Machines, NC, P-completeness)
- An introduction to randomized computation (time permitting)
Marking scheme
| Component | EECS4115 | EECS5115 |
| Homework exercises | 25% | 25% |
| Test 1 | 10% | 10% |
| Test 2 | 15% | 10% |
| Oral test | 10% | 10% |
| Participation | 10% | 10% |
| Project (EECS5115 only) | 0% | 10% |
| Final exam | 30% | 25% |
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 discuss it with me during an office hour.
Announcements
- (Nov 13) Assignment 6 clarification: For part (e), s should be the maximum possible sum of large elements that does not exceed t.
- (Oct 20) As agreed in class today, the date of test 2 is moved to Tuesday, Nov 3.
- (Oct 16) I have to change the time of the office hour on Mon, Oct 19 to 4:00 p.m.
- (Oct 14) Free offer: As a student, you can get a free 1-year membership to the ACM at this link. Reading the monthly magazine Communications of the ACM is a good way for computing professionals to keep up with what's going on in the field.
- (Oct 9) There is a public lecture (via Zoom) on Oct 20 that might be of interest: Are people still smarter than machines?
- (Oct 2) My office hour on Mon, Oct 5 will be moved to Tue, Oct 6 at 2pm.
Important Dates
(Information will be added to this table thoughout the term.)
| First class | September 10 |
| Test 1 | October 1 |
| Reading Week (no classes) | October 10-16 |
| Test 2 | November 3 |
| Drop deadline | November 6 |
| Oral test | Various dates, mid-Nov |
| Bonus Quiz | December 2, 10:00-11:00 |
| Last class | December 8 |
| Exam period | December 9-23 |
References
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.
The textbook website has lists of errata.
Other Books
-
[AB] Sanjeev Arora and Boaz Barak.
Complexity Theory: A Modern Approach.
Cambridge University Press, 2009.
A draft of the book is available online.
-
[BDG] José Luis Balcázar, Josep Diaz, Joaquim Gabarró.
Structural Complexity I, 2nd ed.
Springer, 1995.
Nicely written, accessible introduction. Available online at York Library via SpringerLink.
-
[BC] Daniel Pierre Bovet and Pierluigi Crescenzi.
Introduction to the Theory of Complexity.
Prentice Hall, 1994.
-
[DK] Ding-Zhu Du and Ker-I Ko.
The Theory of Computational Complexity, 2nd ed..
Wiley-Interscience, 2014.
-
[Gol] Oded Goldreich.
Computational Complexity: A Conceptual Perspective.
Cambridge University Press, 2008.
Preliminary versions of this book are available from the author's
website.
-
[HS] Steven Homer and Alan L. Selman.
Computability and Complexity Theory, 2nd ed..
Springer, 2014.
Available online at York Library via SpringerLink.
-
[Imm] Neil Immerman.
Descriptive Complexity.
Springer, 1999.
Emphasizes connections to formal logic.
-
[Pap] Christos Papadimitriou.
Computational Complexity.
Addison-Wesley, 1994.
Very nicely written book that covers a lot of ground.
Original Articles
-
[CR73] S.A. Cook and R.A. Reckhow. Time bounded random access machines, J. of Computer and System Sciences, volume 7, pages 354-375, 1973.
-
[HS65] J. Hartmanis and R.E. Stearns. On the computational complexity of algorithms, Trans. of the AMS, volume 117, pages 285-306, 1965.
Resources for Special Topics
-
[ACG] G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela and M. Protasi.
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties.
Springer, 1999.
Associated with this book is the online Compendium of NP Optimization Problems, which is like a version of Garey and Johnson's appendix (with more emphasis on approximations).
-
[CLRS] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein.
Introduction to Algorithms, 3rd edition.
MIT Press, 2009.
Great general algorithms book, and it has a nice chapter on NP-completeness.
Available online at York Library.
-
[GJ] Michael R. Garey and David S. Johnson.
Computers and Intractability.
W. H. Freeman, 1979.
The bible of NP-completeness.
Johnson has also published a sequence of columns (available here) that form a kind of sequel to the book.
-
[GHR] Raymond Greenlaw, James Hoover, Walter L. Ruzzo.
Limits to Parallel Computation: P-completeness Theory.
Oxford University Press, 1995.
Available online from Ruzzo's web page.
-
[MM] Christopher Moore and Stephan Mertens.
The Nature of Computation
Oxford University Press, 2011.
Wide coverage of the theory of computation, with lots of good examples.
Available online via York Library (although you have to select the catalogue record for the printed copy to get access to its chapters).
-
[SP] Uwe Schöning and Randall Pruim.
Gems of Theoretical Computer Science.
Springer, 1995.
Each chapter presents a beautiful theorem from various fields of computer science (with a number from complexity theory).
Blogs
More advanced complexity resources
-
[Aar] Scott Aaronson (zookeeper).
The Complexity Zoo.
This wiki has information on hundreds of complexity classes.
Its bibliography
includes a huge number of papers on complexity theory.
-
[HO] Lane A. Hemaspaandra and Mitsunori Ogihara.
The Complexity Theory Companion.
Springer, 2002.
Arranges Theorems according to the techniques used to prove them.
-
[RW] Steven Rudich and Avi Wigderson, eds.
Computational Complexity Theory.
AMS and Institute for Advanced Study, 2004.
Lecture notes, starting from some basics, but moving quickly to more advanced topics.
-
[Wig] Avi Wigderson.
Math and Computation.
Unpublished manuscript, 2019.
Available from the author's web page.
-
[Zim] Marius Zimand.
Computational Complexity: A Quantitative Perspective.
Elsevier, 2004.
Focussed on questions of what fraction of problems in a class have certain properties.
Reading
| Date | Section | Suggested Exercises |
| Sep 10 | Review chapter 0 and 3 | 0.1-0.8, 3.1-3.2, 3.7, 3.8, 3.10-3.13 |
| Sep 15 | 7.1, review 3.1 | 7.1, 7.2, 3.8 |
| Sep 17 | review 3.2 | 3.12, 3.13 |
| Sep 17 | notes on Palindromes | Show every single-tape TM that decides {0x1y2x : x,y ≥ 0} takes Ω(n log n) steps |
| Sep 22 | 7.2 | 7.3-7.6, 7.8, 7.9, 7.13, 7.14, 7.15 |
| Sep 24 | 7.3 | 7.7, 7.12, 7.16 |
| Oct 6 | 7.4 | 7.18, 7.20-7.27 |
| Oct 20 | 7.5 | 7.17, 7.28, 7.30-7.33, 7.35, 7.38, 7.40-7.41 |
| Oct 27 | Optional: The Status of the P Versus NP Problem (from CACM, Sep 2009) and/or
P vs. NP survey results (from SIGACT News, Mar 2019; starts on p.4) | |
| Nov 5 | 10.1 | |
| Nov 10 | 8.0-8.1, 8.4 | 8.1, 8.4, 8.7, 8.9, 8.17, 8.20, 8.22 |
| Nov 12 | 8.5, 8.6 | 8.25,8.29,8.32 |
| Nov 19 | 8.2, 8.3 | 8.3,8.4,8.6,8.11,8.15 |
| Nov 24 | 9.1 (to page 371) | 9.1-9.3,9.12,9.13 |
| Dec 1 | p.396-398, Defn 10.10 | 10.7, 10.11, 10.19, 10.20, 10.22 |
NOTE: Exercise numbers are from the third edition of the textbook.
Course Handouts
Updated December 3, 2020