COSC 545 - Theory of Computation (Spring 2017)

Georgetown University

Prof. Calvin Newport

Tuesday and Thursday, 11:00 am to 12:15 pm

Maguire 101

Course Overview

Description

This course covers foundational results in theoretical computer science, with a focus on how we model computation and how we use these models to explore key questions about what can and cannot be solved (efficiently) with computing devices. Many of the concepts in this course will come up often in the life of a computer scientist (e.g., NP-completeness, decidability, grammars, etc).

During the final lectures of the course, we will tackle some cutting edge topics from the field (time permitting), to provide guidance to those who might be interested in pursuing research in this topic in graduate school.

This course is open to PhD and Masters students. Because our department doesn't regularly offer a theory course at the undergraduate level, I'm also happy to allow advanced undergraduates to enroll with my permission.

Textbook

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

Grading

Grades in the course will be based on five problem sets and two exams.

In determining your final grade, I will add up the total number of points you earned and assign your grade based on this sum. (The mapping from point totals to letter grades is something I develop as the semester progresses and I get a better sense of the relative difficulty of the problems I assigned. If you are unsure how you are doing in the class, please ask me.)

The point values of the exams and problem sets are calibrated so they they contribute approximately the following percentage toward your final point total:

Problem sets50%
Midterm25%
Final25%

 

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:

Course Logistics

Office Hours

I hold regular office hours in my office at 334 Saint Mary's Hall from 12:30 to 2:00 on Thursdays.

Problem Sets

Problem sets will be posted for download on the schedule below on the day they are assigned. Detailed sample solutions and notes will be handed back to students along with the graded problem sets. I try to grade and return problem sets within one week.

The following rules describe my expectations and grading policies for problem sets:

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 current schedule for the course (some changes may occur during the semester). Problem sets will be posted for download on the schedule as they become available. The readings column lists the chapters from the Sipser textbook that cover the corresponding lecture's material.

Class NumberDateDescription Readings
Part 1: Automata Theory
11/12Intro; finite automata 1.1
21/17Non-determinism; regular languages; 1.2, 1.3
31/19Pumping lemma for regular languages; context-free grammars; Chomsky normal form1.4, 2.1
41/24Pushdown automata; pumping lemma for context-free languages2.2, 2.3
51/26Context-free languages 3.1
Part 2: Computability Theory
61/31Turing machines
  • pset 1 due
  • pset 2 available [Download]
4.1
72/2Some decidable and recognizable languages. Proof of undecidable and unrecognizable languages.4.1, 4.2
82/7Reducibility5.1, 5.3, 6.3
92/9Turing machines (cont) 5.1, 5.2
102/14Reductions 6.1
112/16Reductions (cont), LBAs, Recursion theorem  
122/21Lecture overflow; midterm review
  • pset 2 due
 
132/23Midterm 7.1
Part 3: Complexity Theory
142/28Time complexity; the classes P and NP 7.2, 7.3
153/2NP-completeness; the Cook-Levin theorem 7.4
 3/7No Class: Spring Break 
 3/9No Class: Spring Break 
  Snowday distruption... 
163/21Cook-Levin theorem; more NP-complete problems7.4, 7.5
173/23Space Complexity; SPACE and NSPACE complexity classes 8.0
183/28Savitch's Theorem; PSPACE and PSPACE-Completeness
  • pset 3 due
  • pset 4 available
8.1, 8.2, 8.3
193/30Games and Generalized Geography; 8.3
204/4L and NL, NL-Completeness, and NL = coNL8.4, 8.5, 8.6
214/6Hierarchy Theorems 9.0, 9.1
224/11Relativization
  • pset 4 due
  • pset 5 available
9.0, 9.2
 4/13No Class: Easter Break 
234/18Approximation Algorithms10.1
244/20Probabilistic Computation, BPP; advance topic (time permitting)
  • pset 5 due
10.2
254/25Lecture overflow; final exam review  
 4/27No Class
  • Last day for graduate students to withdraw.
 
 5/5 to 5/13Final exam period (the date, time, and location of exam will be posted by the registrar during the semester.)