COSC 545 - Theory of Computation (Spring 2013)

Georgetown University

Prof. Calvin Newport

Tuesday and Thursday, 3:30 - 4:45

Intercultural Center, Room 211B

Course Overview

Description

This course covers foundational results in theoretical computer science. Approximately the first half of the course will focus on finite automata and computability theory, with the remainder focused on complexity theory.

Students will come way from this course familiar with the classic concepts from theoretical computer science (language types, what you can and cannot solve with computers, the complexity of problems, including NP-completeness, and so on). Students will also develop comfort formally proving things both possible and impossible.

Textbook

The required textbook for this course is Introduction to the Theory of Computation, 3rd Edition, Michael Sipser, 2012. Most of the topics covered in this course, and many of the problem set problems, will be drawn from this text.

Grading

Grades in the course will be based on biweekly problem sets, two exams, and participation. The participation grade will be based on your attendance and involvement in class. If you show up to class, pay attention, and ask questions when stuck (either in class, or after class), you will get full participation points.

In determining your final grade, I will calculate the percentage of available points you received for your problem sets, exams, and participation, and then combine these percentages with the following weights:

Problem sets	50%
Midterm	20%
Final	20%
Participation	10%

Every student will therefore end up with a single weighted point percentage. Toward the end of the course, I will decide the mapping from ranges of these values to letter grades. Feel free to check in with me earlier in the semester, however, for an estimate of where you stand.

How to Get an A in this Course (without Burning Out)

A few tips for doing well in this course without excessive amounts of stress:

• To save time, do not read the textbook before lecture. Instead, pay careful attention during class and then go back and use the textbook to fill in only what you did not understand.
• Learn the material the same week it is presented (using your textbook, your classmates, and me to help understand what confuses you). If you do this, studying for the exams will amount to a tractable review. If you do not do this, studying will devolve into a mind-numbing slog.
• Start problem sets early. Work systematically in focused bursts. Expect to need multiple sessions to finish the assignments. My general strategy as a graduate student, for example, was to never spend more than two hours on any given day on any given problem set. (See this article for more advanced problem set strategies.)
• I am always happy to chat about the tactical side of succeeding as a graduate student (time management, study skills, etc.). Feel free to come to office hours to talk shop on these issues.

Course Logistics

Office Hours

I hold regular office hours from 11:30 am to 1:00 pm on Thursdays, in my office at 342 A Saint Mary's Hall. If this time conflicts with your class schedule, let me know, and we can arrange alternate meetings as needed.

Contact

To ask me small logistical questions, I prefer that you grab my attention immediately before or after class. For substantive content questions, I prefer that you bring them to office hours. Use e-mail only when the above two options are not applicable.

Problem Sets

The following rules will help keep the problem set submission and grading process running smoothly:

• You must work alone on problem sets. You may only discuss problems with me. The only materials you can reference when working on these problems are your course notes and the assigned textbook. In particular, you may not reference online sources, solutions from previous classes, or talk to other students when working on problem set problems.
• Problem sets should be handed in at the beginning of class on the day they are due. That is, bring a physical copy of the problem set to class to give to me before the lecture begins.
• Problem sets not handed in by the beginning of lecture will be considered late, and 10% of the points deducted. Problem sets not handed until the day after the deadline will have an additional 10% deducted (slide late problem sets under my door if I am not in my office). Beyond this point, problem sets will not be accepted.

Exams

There will be two exams in the course: a midterm and a final. The midterm covers automata and computability theory and the final covers complexity theory (i.e., it is not cumulative).

Academic Integrity

I take academic integrity seriously. To repeat the problem set instructions from above: You must work alone on problem sets. You may only discuss problems with me. The only materials you can reference when working on these problems are your course notes and the assigned textbook. In particular, you may not reference online sources or talk to other students.

You may not bring any outside material into exams.

You may not reference any problem sets, exams, or solutions from prior teachings of this course.

When in doubt, ask me what is allowed.

Schedule

Below is the tentative schedule for the course. I will modify the schedule as needed as the course progresses. Problem sets will be posted below on this schedule as they become available. The readings column lists the chapters from the Sipser textbook that cover the corresponding lecture's material.

Class Number	Date	Description	Readings
		Part 1: Automata Theory
1	1/10	Intro; finite automata	1.1
2	1/15	Non-determinism; regular languages; pset 1 available [Download]	1.2, 1.3
3	1/17	Pumping lemma for regular languages; context-free grammars; Chomsky normal form	1.4, 2.1
4	1/22	Pushdown automata; pumping lemma for context-free languages	2.2, 2.3
		Part 2: Computability Theory
5	1/24	Turing machines	3.1
6	1/29	Decidable languages; file look-up machine; pset 1 due pset 2 available [Download]	4.1
7	1/31	Undecidable and Unrecognizable languages	4.2
8	2/5	Reducibility	5.1, 5.3, 6.3
9	2/7	Linear-bounded automata; PCP	5.1, 5.2
10	2/12	Advanced topics in computability theory: recursion theorem; pset 2 due	6.1
11	2/14	Lecture overflow; midterm review
12	2/19	Midterm pset 3 available (Note: due to spring break, you have less time than normal to complete this problem set; accordingly, it is shorter than normal problem sets.)
13	2/21	Advanced topics in computability theory: decidability of logical theories, Godel's incompleteness theorem, and the computational complexity of information	6.2, 6.4
		Part 3: Complexity Theory
14	2/26	Time complexity; TIME and NTIME complexity classes	7.1
15	2/28	The classes P and NP pset 3 due	7.2, 7.3
	3/5	No Class: Spring Break
	3/7	No Class: Spring Break
16	3/12	NP-completeness; the Cook-Levin theorem; pset 4 available [Download]	7.4
17	3/14	More NP-complete problems	7.4, 7.5
18	3/19	Space Complexity; SPACE and NSPACE complexity classes	8.0
19	3/21	Savitch's Theorem; PSPACE and PSPACE-Completeness	8.1, 8.2, 8.3
20	3/26	Games and Generalized Geography; pset 4 due pset 5 available [Download]	8.3
	3/28	No Class: Easter Break
21	4/2	L and NL, NL-Completeness, and NL = coNL	8.4, 8.5, 8.6
22	4/4	Hierarchy Theorems	9.0, 9.1
23	4/9	Intractable Problems; pset 5 due pset 6 available [Download]	9.0, 9.2
24	4/11	Approximation Algorithms	10.1
25	4/16	Probabilistic Computation, BPP	10.2
26	4/18	Lecture overflow/advanced topic
27	4/23	Advanced topic pset 6 due
28	4/25	Review for final examination
		Final examination (date and location pending)

Qualifying Exam

The PhD qualifying exam includes a segment on theory of computation. It is based on the material covered in COSC 545 (which is summarized in the schedule below along with the corresponding chapters of the Sipser textbook). To help your review, here is a summary of what you are expected to know from this material for the qualifying exam:

• From Part 1 of the Course: You should be comfortable proving that languages are and are not regular and/or context-free. This includes familarity with all equivalent models for these language classes and the regular language pumping lemma.
• From Part 2 of the Course: You should be comfortable with the definitions of different Turing Machine models and the Turing decidable and Turing recognizable language classes. In addition to proving that languages are decidable and/or recognizable, you might also be asked to prove problems not decidable and/or not recognizable using standard reductions and mapping reductions. Your reduction tool kit should include the computation history method.
• From Part 3 of the Course: You should be comfortable with analyzing time complexity and working with the complexity classes TIME, NTIME, P, and NP. You should be comfortable proving problems are NP-complete. In addition, you should be comfortable analyzing space complexity and working with the complexity classess SPACE, NSPACE, PSPACE, L, NL, and co-NL. Finally, you should know the main space and time hierarchy theorems, but not necessarily the details of their proofs.