Fall'25: Undergraduate Computability and Complexity Theory (CS 452)

Monday: 19:30-20:50
Wednesday: 19:30-20:50
Pharmacy - Room 115

Instructor: Karthik C. S. (Office hours at Core Building, Room 308: Monday, 14:00-15:00)

Recitations: Mursalin Habib (SEC - Room 210 on Wednesdays from 12:25-13:20).

Homework


All homework must be typeset in Latex. Otherwise the homework will not be evaluated.

Each homework has 10 points for presentation. If your homework is very hard to read, these points will be entirely deducted.

Homework 1 is due on 09/29. Homework 2 is due on 11/03. Homework 3 is due on 12/10.

You are free to discuss about the questions in the homework with other students and even take some help from the TA during recitations, but must write the solutions on your own.

Grading


Your grade is computed out of 1000 points (you may accumulate at most 1000 points; if you obtain more than 1000 points then it will be capped to exactly 1000 points).

Midterm I is 250 points, Midterm II is assigned 350 points, and the final exam is assigned 450 points.

Homework I is 200 points, Homework II is assigned 300 points, and Homework III is assigned 400 points.

A majority of the questions in Midterm I (respectively Midterm II and final exam) will be taken from Homework I (respectively Homework II and Homework III).

Your grade will be computed solely based on the points acquired through homework, midterms, and final exam. There are no other extra credits activities for the course. No exceptions.

Your final points accumulated is maximum(Homework I, Midterm I) + maximum(Homework II, Midterm II) + maximum(Homework III, Final Exam).

There is no curve: you must earn a minimum of 90% of the total points for an A (900 points), 85% for a B+ (850 points), 80% for a B (800 points), 75% for a C+ (750 points), 70% for a C (700 points), and 60% for a D (600 points). You will fail the course if you earn less than 60% points (600 points).

The cutoffs are strictly followed for each letter grade. A computed grade of 74.99% is a C not a C+. There are no other extra credits activities for the course. No exceptions.

For all the 3 exams the following scaling policy will be applied. If the total points that can be accumulated through a specific exam is X and if the 70 percentile score obtained on the exam is x which is in the interval [1,0.9X], then everyone’s score will be scaled by a multiplicative factor of (9X)/(10x). For example, if the 70 percentile score obtained on the exam across all students is 100 out of 150 points, then every single student’s score will be multiplied by a factor of 1.35. Therefore, if you obtained 80 points, then it will be scaled up, and your new score will be 108 points (because 80 × 1.35 = 108). These bonus points are given to counter if the exam is too hard.

Tentative Topics and Schedule


Lecture # When Topic
Lecture 1 09/03 Diagonalization and Gödel's Incompleteness Theorems
Lecture 2 09/08 Finite Automata and Regular Languages
Lecture 3 09/10 Regular Operators and NFA
Lecture 4 09/15 Equivalence of NFA and DFA
Lecture 5 09/17 Regular Expressions
Lecture 6 09/22 Pumping Lemma for Regular Languages
Lecture 7 09/24 Context Free Grammar, Ambiguity, and Chomsky Normal Form
Lecture 8 09/29 Summary of Lectures 1-6
10/01 Midterm I
Lecture 9 10/06 Push Down Automata
Lecture 10 10/08 Equivalence of CF Grammars and PDA
Lecture 11 10/13 Pumping Lemma for Context Free Languages
Lecture 12 10/15 Turing Machines and Decidability
Lecture 13 10/20 Undecidable Problems
Lecture 14 10/22 Halting Problem and Rice's Theorem
Lecture 15 10/27 Complexity Theory: Formalism
Lecture 16 10/29 P, NP, NP-Completeness
Lecture 17 11/03 Summary of Lecture 7, 9-14
11/05 Midterm II
Lecture 18 11/10 Cook-Levin Theorem I
Lecture 19 11/12 Cook-Levin Theorem II
Lecture 20 11/17 Natural NP-Complete Problems I
Lecture 21 11/19 Natural NP-Complete Problems II
Lecture 22 11/24 Hardness of Approximation
Lecture 23 12/01 Fine-Grained Complexity I
Lecture 24 12/03 Fine-Grained Complexity II
Lecture 25 12/08 Communication Complexity and Related Topics
Lecture 26 12/10 Summary of Lectures 15-16, 18-25
12/xx Final Exam