CSCI 313: Theory of Computation

General Information

Lecture: MWF 4:00-5:00 pm Parmly 405

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

This book is expensive, but there is a free version for students available online. Make sure to get the third edition!

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

- Two in-class or exams: total 30%
- Comprehensive final exam: 20%
- Homework assignments: 50%

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, or copy material you find online. Start each assignment well before it is due so that if you have trouble with it, you can get help from me during office hours.

Accommodations

Washington and Lee University makes reasonable academic accommodations for qualified students with disabilities. All undergraduate accommodations must be approved through the Office of the Dean of the College. Students requesting accommodations for this course should present an official accommodation letter within the first two weeks of the (fall or winter) term and schedule a meeting outside of class time to discuss accommodations. It is the student’s responsibility to present this paperwork in a timely fashion and to follow up about accommodation arrangements. Accommodations for test-taking should be arranged with the professor at least a week before the date of the test or exam.

Final Exam

The final exam for this course will be given during the final exam week. The exam will be distributed electronically for you to complete in no more than three hours. You can return the exam to me via github.

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, 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 has a complete LaTex example, including graphics.

Schedule

	Monday	Wednesday	Friday
05 Sep Week 0			Course Outline
12 Sep Week 1	Math review	Math review	Chapter 1: Finite Automata
19 Sep Week 2	Nondeterminism	Regular Expressions Due: Assignment #1	Regular Expressions
26 Sep Week 3	Regular Expressions	Equivalence of Regular Expressions and DFAs	Equivalence of Regular Expressions and DFAs
03 Oct Week 4	Nonregular languages / Pumping LemmaDue: Assignment #2	Pumping Lemma	Chapter 1 Review
10 Oct Week 5	Exam 1	Exam 1 review	Reading day; no class
17 Oct Week 6	Chapter 2: Context-free grammars and languages Ambiguity	Pushdown Automata	Equivalence of CFG’s and PDA’s CFG ⇒ PDA PDA ⇒ CFG
24 Oct Week 7	Non-context-free languages / CFL Pumping Lemma Due: Assignment #3	Chapter 2 recap	Exam 2
31 Oct Week 8	Chapter 3: The Church-Turing Thesis A TM that decides 0^2ⁿ	A TM that decides connected graphs.	Turing machine variants
07 Nov Week 9	Chapter 4: Decidability Decidability of Regular and CF Languages Due: Assignment #4	Decidability of Regular and CF Languages	Undecidability
14 Nov Week 10	Diagonalization Halting problem utm.py	Halting problem Due: Assignment #5	Halting problem
28 Nov Week 11	Chapter 7: Time complexity The class P	Examples of problems in P Optional Exam 3 Due	O (n³) parsing
05 Dec Week 12	The class NP	Simpsons: P=NP, ??? Due: Assignment #6	Review for final exam