### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1 hour / session

### Prerequisites

### Course Description

This course emphasizes computability and computational complexity theory. Topics include regular and context-free languages, decidable and undecidable problems, reducibility, recursive function theory, time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

### Course Outline

- Automata and Language Theory (2 weeks)
- Finite automata, regular expressions, push-down automata, context-free grammars, pumping lemmas.

- Computability Theory (3 weeks)
- Turing machines, the Church-Turing thesis, decidability, the halting problem, reducibility, the recursion theorem.

- Complexity Theory (7 weeks)
- Time and space measures of complexity, complexity classes P, NP, L, NL, PSPACE, BPP and IP, complete problems, the P versus NP conjecture, quantifiers and games, hierarchy theorems, provably hard problems, relativized computation and oracles, probabilistic computation, interactive proof systems.

### Online Course Format

This course is offered entirely online while the MIT campus is shut down due to the Covid-19 pandemic. Lectures are offered live online via Zoom. The lectures are also recorded for viewing at a later time to accomodate students who cannot participate in the live lectures due to time-zone differences or other reasons. Weekly TA-led recitations are offered both live online and in person, at various times.

Following student recommendations, we can de-emphasize (but not eliminate) the midterm and final exams by adding graded live mini-quizzes for credit during the lectures, to be conducted via Zoom’s polling feature. For students viewing a recorded lecture, an alternate timed and graded recorded mini-quiz will be available, but it must be completed within 24 hours of the original live lecture. Students may chose whether to take the live mini-quiz or the recorded mini-quiz on a lecture-by-lecture basis, and if both are taken for any given lecture, the higher score will be used. We expect that all students will complete the exams and mini-quizzes on their own individually, without assistance from others.

### Textbook

Sipser, Michael. *Introduction to the Theory of Computation*. 3^{rd} ed. Cengage Learning, 2012. ISBN: 9781133187790.

You may use the second edition, but it is missing some additional practice problems. Errata for 2^{nd} edition of textbook.

We will cover Chapters 1, 2 (except 2.4), 3, 4, 5, 6.1, 7, 8, 9.1, 9.2, 10.2 (except the part on Primality), and 10.4 through Theorem 10.33.

### Recitations

Recitations are primarily for going over lecture material in more detail with additional examples and for answering questions. Recitation attendance is optional, and you may attend any recitation you wish. BUT, if you are having trouble, we expect you to attend recitations weekly, and active participation may improve low grades.

### Grading

ACTIVITIES | PERCENTAGES |
---|---|

Homework | 35% |

Quizzes | 25% |

Midterm Exam | 15% |

Final Exam | 25% |

#### Homework

35% of grade. There will be 6 biweekly problem sets. Cooperating on homework is allowed and may be helpful, but you are strongly encouraged to spend some time thinking about each problem yourself first. Solutions must be written up individually (not copied). Using course bibles or other outside or online materials is not permitted.

#### Quizzes

25% of grade. Given during each live lecture and following each recorded lecture.

#### Exams

One midterm (15% of grade) during a class session and one final exam (25% of grade) during finals week. The exams are both open book and open notes. You may only use the class textbook and notes you took in lectures and in recitation.