CSCI 313: Theory of Computation


General Information

Professor: Simon D. Levy
Lecture: MWF 1:25 - 2:20 Parmly 404
Office: Parmly 407B
Office Phone: 458-8419
E-mail: simon.d.levy@gmail.com
  Office Hours: Daily 2:30-4:30 and by appointment

Textbook: Michael Sipser, Introduction to the Theory of Computation, second edition, Thompson Course Technology, 2005

This book is expensive, but far superior to any of the alternatives. You are welcome to use a previous edition, but make sure to check with me to be sure that the exercises match the ones I have assigned.


Brief Overview

This course deals with the mathematical theory of computing. This involves an increasingly powerful series of abstract models of computing "machines". Working hand in hand with these models is an increasingly powerful series of formal languages. The connection between the models and their corresponding languages is investigated. A widely accepted notion of what it means to say that a problem or function is computable is developed and the limitations of computing are explored. Also, an idea of "practical computability" as opposed to theoretical computability is studied. While the course is theoretical by nature, it is important and profitable to note that many techniques that can be used in everyday computer science are covered along the way. An attempt will be made to emphasize applications to areas ranging from hardware design to compiler construction.

At many schools, the theory course is the one that students hate and have the most difficulty with, because it involves a lot of math. This is extremely unfortunate, because the material is genuinely interesting and connects directly with nearly everything else you have done or will do as a computer scientist. I am far more interested in making sure that you understand the material than I am in putting you through a "boot camp" where you sink or swim based on your mathematical background or ability to solve tricky problems. What this means is that you can do well in this class if you do the reading, attend the lectures, start the assignments early, and participate fully. As a non-theoretician, I sometimes find that students who are doing those things will correct me when I make a mistake in class: in other words, this class works best when we all learn together.


Grading

These percentages are flexible. If you have a really hard time on a homework assignment, I'll probably just drop that grade. If you do well on everything but one exam, I'll reduce the impact of that exam on your final grade.

The grading scale will be 93-100 A; 90-92 A-; 87-89 B+; 83-86 B; 80-82 B-; 77-79 C+; 73-76 C; 70-72 C-; 67-69 D+; 63-66 D; 60-62 D-; below 60 F.


Honor System

All exams will be done without books or notes and without assistance from other people. You may NOT work with another person on the homework assignments. Start each assgnment well before it is due so that if you have trouble with it, you can get help from me during office hours.


Homework Assignments

Perhaps the most important aspect of the course is the homework assignments you do. Note that this counts for a substantial part of your course grade. Homeworks will be due in your Sakai dropbox folder (as a PDF email attachment) on 11:59 PM of the due date. No late work, hand-written work, or Word/PowerPoint documents will be accepted, and you will lose 10% immediately if your name does not appear on the document when it is printed out. Serious problems (health / family / personal emergencies) that interfere with attendance / homework should be handled through the Office of the Dean.

Though you don't have to use LaTex to create your PDFs, I encourage LaTex as a useful skill. The first assignment below has a complete LaTex example, including graphics.

  1. Assignment #1

  2. Assignment #2

  3. Assignment #3

  4. Assignment #4

  5. Assignment #5

  6. Assignment #6

  7. Assignment #7

Tentative Schedule of Lectures, Assignments, and Exams

 

Monday

Wednesday

Friday

12 Jan
Week 1
Course Intro Chapter 1
Finite Automata
Finite Automata
19 Jan
Week 2
Nondeterminism Regular Expressions

Due: Assignment #1
Regular Expressions
26 Jan
Week 3
Regular Expressions Equivalence of Regular Expressions and DFAs Equivalence of Regular Expressions and DFAs

02 Feb
Week 4
Nonregular languages /
Pumping Lemma

Due: Assignment #2

Pumping Lemma

Chapter 1 Review
09 Feb
Week 5
Exam 1 Chapter 2:
Context-free grammars and languages

Ambiguity

Context-free grammars and languages
16 Feb
Week 6
Equivalence of CFG's and PDA's
CFG ⇒ PDA   PDA ⇒ CFG

Equivalence of CFG's and PDA's

Due: Assignment #3
Non-context-free
languages
02 Mar
Week 7
Review chapter 2
Chapter 3: The Church-Turing Thesis
A TM that decides 02n

Exam 2
09 Mar
Week 8
Turing machine variants A TM that decides connected graphs. SSA Conference: No class
16 Mar
Week 9
Chapter 4: Decidability

Decidability of Regular
and CF Languages

Due: Assignment #4

Decidability of Regular
and CF Languages

Undecidability
23 Mar
Week 10
Halting problem

utm.py

Due: Assignment #5

Halting problem Chapter 7:
Time Complexity
30 Mar
Week 11
Time complexity
The class P

Examples of
problems in P

Due: Assignment #6
O(n3) parsing
06 Apr
Week 12
The class NP Simpsons:   P=NP,   ??? Due: Assignment #7
Exam 3