**CS 151: Complexity Theory (Spring 2021)**

Instructor: Chris Umans

Office: Annenberg 311

Times: Tu/Th 1:00-2:25 via Zoom

TAs: Vinayak Kumar and Mayank Pandey

Office hours: Zoom links are on the Canvas course page. All times are Pacific Time.

- Wednesdays 2-3pm (Chris)
- Wednesdays 6-7pm (Vinayak)
- Wednesdays 8-9pm (Mayank)

Announcements:

- The third problem set has been posted. It is due Thursday, April 22, at 1pm PST.
- The solutions for PS2 are posted. Please do not consult them until you have turned in the set.

Handouts:

Lecture slides:

- Lecture 1: intro; languages, complexity classes, Turing Machines (pptx, pdf)
- Lecture 2: reductions and completeness, time and space classes, hierarchy theorems, relationships between classes (pptx, pdf)
- Lecture 3: a P-complete problem, padding and succinctness, nondeterminism, NP- and NEXP- complete problems (pptx, pdf)
- Lecture 4: NTIME hierarchy theorem, Ladner's Theorem, unary languages and NP (pptx, pdf)
- Lecture 5: nondeterministic space classes, STCONN, Savitch's Theorem, I-S Theorem, nonuniformity and advice (pptx, pdf)
- Lecture 6: NC hierarchy, formula lower bound on Andreev function (pptx, pdf)

Problem sets:

- Problem Set 1: (pdf, LaTeX source) Solutions (pdf)
- Problem Set 2: (pdf, LaTeX source) Solutions (pdf)
- Problem Set 3: (pdf, LaTeX source)

Resources:

- Here is a LaTeX template (tex, pdf) that you can use for your writeups if you wish.
- all 2017 lectures as a .tar.gz archive.
- Videos of 2019 lectures (Caltech only) here.