CS4510 Automata and Complexity

Spring 2023 3:30-4:45PM Howey L4

People

Course Information

This course answers two main questions:

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 a computation? What even is a computer? Are all problems solvable? We will explore several models of computation and explore their 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.

Other schools may call a version this course something like "Great Ideas in Computer Science". I like to think of it like, a kind of finale to your CS degree. This is the course where you will learn why computer science gets to be called a science.

This course has a lot of preqs, 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. We will follow the book very closely, and the places we differ from the book will be explicitly mentioned.

Evaluation

Schedule

This is subject to change as I realize what takes more or less time.

Date Subject Notes
Jan 09. Introduction notes
Jan 11. Nondeterminism notes
Jan 18. Regexes notes
Jan 23. The Pumping Lemma notes
Jan 25. Context Free Grammars notes
Jan 30. Chomsky Normal Form
Feb 01. Exam 1 Review
Feb 06. Exam 1
Feb 08. Pumping Lemma for CFLs
Feb 13. Pushdown Automata
Feb 15. Equivalence of PDAs and CFGs
Feb 20. Turing Machines
Feb 22. Church-Turing Thesis
Feb 27. Countability
Mar 01. Exam 2 Review
Mar 06. Exam 2
Mar 08. Foundations of Mathematics
Mar 13. Undecidability by Reduction
Mar 15. Post's Correspondence Problem
Mar 27. Kolmogorov Complexity
Mar 29. Complexity Classes
Apr 03. Cook-Levin Theorem
Apr 05. Exam 3 Review
Apr 10. Exam 3
Apr 13. Savitch's Theorem
Apr 17. Reletivization
Apr 19. P/poly
Apr 24. Circuit Lower Bounds

Statement of Intent for Classroom Inclusivity

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.