Harvard CS 221: Computational Complexity (Spring 2018)

General Info:
  • Lecturer: Madhu Sudan;  MD 339; email: first name at cs dot harvard dot edu; Office Hours: TuTh 5-6pm (tentative)
  • TF: Preetum Nakkiran: MD 334; email first name at cs dot harvard dot edu; Office hours and location: TBD.
  • Lecture Time and Location: TuTh 1:00-2:30pm; Room MD 221.

Other links for the course:

Announcements:

  • PS2 (tex, pdf). Due Feburary 16 at 8pm. Submission link.
  • PS1 (tex, pdf).
  • Sign up for the course on Piazza. This will be principal forum for discussions and announcements. If you do not have a harvard email, send mail to Madhu to get enrolled.
  • Canvas will be the main mechanism for submitting psets and getting them graded. If you are not (yet) on canvas, submit your psets by email till you get added to canvas.
  • Sign up for scribing! Signup sheet here. Template for scribing (preamble, lect01.tex).

Topics (Tentative), Calendar and Handouts:

  • Lecture 01 (Tue. 01/23): Introduction. Review of Complexity. Notes. Scribe Notes (tex, pdf).
  • Lecture 02 (Thu. 01/25): Diagonalization. Time/Space Hierarchy. Relativization. Notes. Scribe Notes (tex, pdf).
  • Lecture 03 (Tue. 01/30): Circuits and Formulas. Circuit size vs. Time Complexity. Branching Programs and Space. Counting arguments. Neciporuk bound. Notes. Scribe notes (tex, pdf).
  • Lecture 04 (Thu. 02/01): Non-determinism. Circuit Sat. P vs. NP. Cook vs. Karp reductions. NP vs. CoNP. Notes. Scribe notes (tex, pdf).
  • Lecture 05 (Tue. 02/06): Space Complexity. PSPACE, L, NL, Savitch's theorem. NL=CoNL. Notes. Scribe notes (tex, pdf).
  • Lecture 06 (Thu. 02/08): Alternation. Time vs. Space vs. Alternation. Fortnow's theorem. Notes. Scribe notes (tex, pdf).
  • Lecture 07 (Tue. 02/13): Alternation contd.: Debates, Polynomial Hierarchy, Karp-Lipton Theorem. Notes.
  • Lecture 08 (Thu. 02/15): Randomness. Promise problems. Randomized complexity classes: ZPP, RP, CoRP, BPP.
  • Monday 02/19: Presidents' Day Holiday
  • Lecture 09 (Tue. 02/20): BPP is contained in P/Poly intersect PH: Pairwise independence and hashing!
  • Lecture 10 (Thu. 02/22): Counting problems. #P. Permanent is #P-complete.
  • Lecture 11 (Tue. 02/27): Complexity of Unique-SAT. Approximate counting in PH.
  • Lecture 12 (Thu. 03/01): Parity is not in AC0.
  • Lecture 13 (Tue. 03/06): Toda's Theorem - I
  • Lecture 14 (Thu. 03/08): Toda's Theorem - II
  • Sat. 3/10- Sun 3/18: Spring break
  • Lecture 15 (Tue. 03/20): Interaction. IP, AM, MA.
  • Lecture 16 (Thu. 03/22): IP = PSPACE - I
  • Lecture 17 (Tue. 03/27): IP = PSPACE - II
  • Lecture 18 (Thu. 03/29): Zero Knowledge
  • Lecture 19 (Tue. 04/03): Probabilistically Checkable Proofs. Inapproximability.
  • Lecture 20 (Thu. 04/05): PCP Theorem and proof idea.
  • Lecture 21 (Tue. 04/10): Unique Games, Raghavendra's theorem, SOS Complexity.
  • Lecture 22 (Thu. 04/12): ETH, SETH and Fine-grained Complexity - I
  • Lecture 23 (Tue. 04/17): ETH, SETH, and Fine-grained Complexity - II
  • Lecture 24 (Thu. 04/19): Student Projects.
  • Lecture 25 (Tue. 04/24): (last lecture) TBD

Reference Materials: