General Information

• Instructor: Toniann Pitassi email: tp2684@columbia.edu; OH: Tues 5-6, CSB 513
• Class Time/Place: Fridays: 1:30-4:10 415 Schapiro
• Textbook: Introduction to the Theory of Computation, by M. Sipser
• For some lectures we will follow Lectures in Computational Complexity of Jin-Yi Cai and the book Computational Complexity: A Modern Approach of Sanjeev Arora and Boaz Barak.
• Lecture topics and homeworks are posted on the Lectures/Weekly Info page

Teaching Assistants

• Conlan Olson, email: co2583@columbia.edu; OH: Wed 4-5, Location: CSB 453
• Rain Yang, email: ry2553@columbia.edu; OH: Wed 5-6, Location: CSB 453

Quick Links

• Lectures/Weekly Info: Schedule of lectures, tests/quizzes, and homeworks, links to readings and lectures.
• Courseworks: Has links to a range of resources including the Video Library (for course videos), and Gradescope.
• Gradescope: Submit assignments and view grades here. (You can set up Gradescope by clicking the "Gradescope" module on Courseworks.)
• EdStem: Discussion board (check regularly for announcements).

Course Description:

In this course, we study Computational Complexity, one of the most active areas of theoretical Computer Science, devoted to understanding the intrinsic computational hardness of problems, and the limitations of efficient algorithms. Along the way we will uncover some very important ideas, including: connections between computational hardness and randomness, and between computational hardness and cryptography; Below is a list of topics we plan to cover in the course:

• Time complexity classes (P, NP, PH, EXP), Reductions and Complete problems.

• Space complexity classes (Logspace, NL, RL, PSPACE). Graph connectivity, Catalytic Space

• Interactive proofs, IP=PSPACE.

• Randomized complexity classes BPP, RP; randomness in crypto/privacy; hardness vs randomness.

• Boolean circuit and formulas. Lower bounds for constant-depth circuits.

• Communication complexity.

• Approximation algorithms, PCP theorem.

Prerequisites

• An introductory course on theory of computation, e.g., COMS 3261. In particular you should be familiar with Turing machines, decidability, and the complexity classes P and NP, at the level of Chapters 3,4,7 of Sipser, Introduction to the Theory of Computation. You should also be comfortable with asymptotic notation (Big-O and Big-Omega), and run-time analysis.
• A course on algorithms will be helpful but not required. This course is mostly theoretical, so you should have a good grasp of discrete math, probability theory and proofs (See Chapter 0 of Sipser's book).

Grading

• Four homeworks (10% total). HWs posted on Wednesdays and due by 11:59pm on the due date (submit thru Gradescope). HW1: Out Sept 23, Due Oct 1; HW2: Out Oct 7, due Oct 15; HW3: Out Nov 2, due Nov 12; HW4: Out Nov 30, due Dec 10.
• Three in-class tests (20% each) (Oct 9, Oct 23, Nov 20) and a final exam (30%) (Dec 18). See Lectures/Weekly Info for important details and more info.
• Please read the Syllabus carefully for information on grading, collaboration, AI policy, and important dates.