Theory of Computation (Fall 2023)

Time and Location: TTh 1:30-2:45pm, Hodson 311

Instructor: Xin Li. Office hours: Wednesday 2:00pm-3:00pm in person, or by appointment

TA: Songtao Mao. Email: Office hours: Friday 2:00pm-4:00pm, by Zoom.


Course description: This is a combined undergraduate upper-level and graduate-level course studying the theoretical foundations of computer science. Topics covered will be models of computation from automata to Turing machines, computability, complexity theory, randomized algorithms, inapproximability, interactive proof systems and probabilistically checkable proofs. Students may not take both 600.431 and 600.631, unless one is for an undergrad degree and the other for grad degree.

Pre Requisite: Discrete math or permission. Probability theory strongly recommended.

Required Textbook: Computational Complexity: A Modern Approach, by Sanjeev Arora and Boaz Barak.
Recommended Textbook: Introduction to the Theory of Computation, by Michael Sipser.

Topics Covered

Further readings

Interactive proof with Perfect Completeness or Soundness

Introduction to mathematical arguments

Some Help on Reading Mathematics and Creating Proofs

A picture of some complexity classes

Wiki page of Hilbert's 10th problem

An article about Alan Turing

A website about Turing and the history of modern computing

Godel's letter to von Neumann

Clay Institute's official page about the P vs. NP problem

Lance Fortnow's exposition of the P vs. NP problem