Professor:
Simon D. Levy Lecture: MWF 9:05  10:00 Parmly 405 Office: Parmly 407B Email: simon.d.levy@gmail.com Office Hours: MWF 10:1011:05, 2:30325, and by appointment 
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 nontheoretician, 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.
The grading scale will be 93100 A; 9092 A; 8789 B+; 8386 B; 8082 B; 7779 C+; 7376 C; 7072 C; 6769 D+; 6366 D; 6062 D; below 60 F.
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.
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 testtaking should be arranged with the professor at least a week before the date of the test or exam.
The exam will be given in Parmly 405, and you should arrive promptly before the appointed time. If you are more than 15 minutes late, you will have to reschedule your exam. If you are more than 15 minutes late to the last exam period on Friday afternoon, you will receive a grade of 0 on your exam.
Students who have approved academic accommodations must make arrangements to use those accommodations directly with the instructor no later than the last day of class. Students approved for extra time will receive that time at the tail end of the morning exam period or before the beginning of the afternoon exam period (for example, ending at 1:30 PM for a morning exam or beginning at 12:30 PM for an afternoon exam). Students approved for a lowdistraction testing location should reserve that space during the last week of classes, following instructions distributed by Dean Price (sophomores, juniors or seniors) or Director of Disability Resources Lauren Kozak (firstyears).
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, handwritten 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.
Monday 
Wednesday 
Friday 

04 Sep Week 0 
Course Outline  
11 Sep Week 1 
Math review  Chapter 1 Finite Automata 
Finite Automata 
18 Sep Week 2 
Nondeterminism 
Regular Expressions Due: Assignment #1 
Regular Expressions 
25 Sep Week 3 
Regular Expressions  Equivalence of Regular Expressions and DFAs 
Equivalence of Regular Expressions and DFAs

02 Oct Week 4 
Nonregular languages / Pumping Lemma Due: Assignment #2 
Pumping Lemma 
Chapter 1 Review 
09 Oct Week 5 
Exam 1 
Chapter 2: Contextfree grammars and languages 
Reading day; no class 
16 Oct Week 6 
Pushdown Automata 
Equivalence of CFG's and PDA's CFG ⇒ PDA PDA ⇒ CFG Due: Assignment #3 
Noncontextfree languages 
23 Oct Week 7 
Review chapter 2 
Chapter 3: The ChurchTuring Thesis A TM that decides 0^{2n} 
Exam 2 
30 Oct Week 8 
Turing machine variants  A TM that decides connected graphs.  Turing machine variants 
06 Nov Week 9 
Chapter 4: Decidability
Decidability of Regular Due: Assignment #4 
Decidability of Regular and CF Languages

Undecidability 
13 Nov Week 10 
Halting problem

Halting problem
Due: Assignment #5 
Halting problem 
27 Nov Week 11 
Chapter 7: Time complexity
The class P 
Examples of problems in P 
O (n^{3}) parsing 
04 Dec Week 12 
The class NP 
Simpsons:
P=NP,
???
Due: Assignment #6 
Review for final exam 