CS 278 Computational Complexity Theory (Spring 2024) 

Course Description

Computational Complexity studies the power and limitations of efficient computation. What can be computed with bounded resources such as time, memory, randomness, communication, and parallel cores? In this course, we will explore these beautiful questions. While most of them are widely open (e.g., Is verifying easier than proving? Is parallelism always helpful? Does randomness help in computation?), we will see many surprising connections between them. The course will be based on selected chapters from the book “Computational Complexity” by Sanjeev Arora and Boaz Barak.

Among the highlights, we will discuss Randomized Algorithms, Bounded-Space Algorithms, Savitch's Theorem, Immerman-Szelepcsényi's Theorem, the PCP Theorem and its connections to Hardness of Approximation, Interactive Proofs and IP = PSPACE, Hardness vs. Randomness, Pseudorandomness and Derandomization, Hardness Amplification, Introduction to Communication Complexity, Karchmer-Wigderson games, Circuit Complexity, Hardness within P.

General Information

Time and Place: Tuesday, Thursday 2:00 - 3:30 PM, Soda 405.

Instructor: Avishay Tal, email: atal "at" berkeley.edu, Office Hours: Thursday 3:30-4:30 PM.

TA: Hongxun Wu, email: wuhx "at" berkeley.edu, Office Hours: Thursday 9:00 - 10:00 AM at Soda 326. 

Grading: Homework assignments - 50% (5 assignments), scribe - mandatory + replaces the lowest-grade hw assignment, Final Project & Presentation - 50%. 

Prerequisite: CS170 or equivalent is required. CS172 or equivalent is recommended.

Pre-Reading:  For those of you who want a refresher on the general setting, or those who haven't taken 172, please see Chapter 3 in Sipser's book ("Introduction to the Theory Of Computation" by Michael Sipser) or Chapters 1 & 2 Arora-Barak. 

Textbooks & Lecture Notes:

Problem Sets

Lecture Notes