This course answers two main questions:
What are the fundamental limits of computation?
What makes some problems easy, and others hard?
The first question is the study of the area of Computability theory. Most of its questions are solved, which is what makes this subject fun. We are concerned with such extremal, almost philosophical questions. What even is computation? What even is a computer? Are all problems solvable? We will explore several models of computation and explore their relative power, and weaknesses.
The second question is the study of Complexity theory. Most of its questions are unsolved. This subject does not have a happy ending (and perhaps won’t, in our lifetimes) but this contrast is what makes it interesting. We may not know how to solve certain questions, but ironically, we know a lot about how hard these questions are.
I like to think of this course as a finale to your CS degree. It is simultaneously the most important and least important course you will take. It is the least important as it doesn’t develop any single technical skill. It is the most important, as it develops your ability to conceptualize and theorize. This is the course where you will learn why computer science gets to be called a science. It puts the rest of your degree into context.
This course has a lot of pre-reqs, some of which I would disagree should be a requirement. All you really need is good proof skills, like those found CS2050. If you think you might be rusty, please refresh chapter zero of the Sipser book.
The book for the course is Introduction to the Theory of Computation by Michael Sipser. It is an excellent textbook, can’t count how many times I’ve read it. The notes and lectures for the course are the authoritative reference, but it is expected you follow along with Sipser’s book. Later on, I may reference the Arora-Barak and Li-Vitanyi books.
This is subject to change.
| Ganesh MW | Ladha TR | Subject | Notes | Other | Video |
|---|---|---|---|---|---|
| 01/06/25 | 01/07/25 | Introduction | NOTES | L01A-B | |
| 01/08/25 | 01/09/25 | Nondeterminism | NOTES | L02A-B | |
| 01/13/25 | 01/14/25 | Regular Expressions | notes | L03A | |
| 01/15/25 | 01/16/25 | The Pumping Lemma | NOTES | L03B | |
| 01/22/25 | 01/21/25 | Context-Free Grammars | notes | L04A-B | |
| 01/27/25 | 01/23/25 | Syntactic Structures | notes | L05A-B | |
| 01/29/25 | 01/28/25 | Push Down Automata | notes | L06A-B | |
| 02/03/25 | 01/30/25 | Equivalence of PDAs and CFGs | notes | L07A | |
| 02/05/25 | 02/04/25 | Turing Machines | slides, required reading1, required reading 2, required reading 3 | ||
| 02/10/25 | 02/06/25 | Exam 1 | notes | L08A | |
| 02/12/25 | 02/11/25 | The Church-Turing Thesis | notes | L08B | |
| 02/17/25 | 02/13/25 | Turing Completeness | notes | L09A-B | |
| 02/19/25 | 02/18/25 | Countability | notes | L10A-B | |
| 02/24/25 | 02/20/25 | Foundations of Mathematics | notes | L11A-B | |
| 02/26/25 | 02/25/25 | Godel Incompleteness | notes | L12A-B | |
| 03/03/25 | 02/27/25 | Undecidability | notes | L13A | |
| 03/05/25 | 03/04/25 | Art of Reduction | notes | L13B | |
| 03/10/25 | 03/06/25 | Posts Correspondence Problem | notes | L14B | |
| 03/11/25 | Kolmogorov Complexity | ||||
| 03/12/25 | 03/13/25 | Exam 2 | |||
| 03/24/25 | 03/25/25 | Complexity Classes | notes | L15A-B | |
| 03/26/25 | 03/27/25 | In and around NP | notes | L16A-B | |
| 03/31/25 | 04/01/25 | In and around PSPACE | notes | L17A-B | |
| 04/02/25 | 04/03/25 | Relativization | notes | L18A-B | |
| 04/07/25 | 04/08/25 | Circuits | notes | L19A-B | |
| 04/09/25 | 04/10/25 | The Polynomial Hierarchy | notes | L20A | |
| 04/14/25 | 04/15/25 | Karp-Lipton Theorems | notes | L20B | |
| 04/16/25 | 04/17/25 | Exam 3 | |||
| 04/21/25 | 04/22/25 | Open Topic | notes |
Besides the notes here, There are additional references:
As a member of the Georgia Tech community, I am committed to creating a learning environment in which all of my students feel safe and included. Because we are individuals with varying needs, I am reliant on your feedback to achieve this goal. To that end, I invite you to enter into dialogue with me about the things I can stop, start, and continue doing to make my classroom an environment in which every student feels valued and can engage actively in our learning community.
Submission of any work not your own can result in anything from a zero on the assignment to a report to OSI.