General Information

• Instructor: Toniann Pitassi Office: 513 Mudd Building
• Time: Fridays: 1:10-3:40
• 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 page

Teaching Assistants

• Conlan Olsan, Office Hours: ? , Location: ? , Email:
• Rain Yang

Quick Links

• Lectures: 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), the Ed Discussion board, and Gradescope.
• Ed Discussion: Forum for asking questions about course material and homework assignments.
• Gradescope: Submit assignments and view grades here. (You can set up Gradescope by clicking the "Gradescope" module on Courseworks.)

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.

• Randomness as a resource; use of randomness in cryptography, privacy; randomized classes (RP, BPP) and hardness versus randomness.

• Nonuniform models: 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.
• You are expected to be familiar with the basic notions of 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 basic run-time analysis of algorithm.
• A course on algorithms will be helpful but not required. This course is mostly theoretical, so you should feel comfortable reading and working with math proofs (Chapter 0 of Sipser's book is a good resource) and general mathematical maturity will be assumed. Some knowledge of discrete mathematics and basic probability (e.g., random variables, expectation, conditional probability, etc.) are required.

Grading

• Four homeworks (20%), two quizzes (20%), midterm (30%) on Oct 23, final exam (30%) during exam period.
• Please read the syllabus Syllabus carefully for information on grading, collaboration, AI policy, and important dates.