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:
- All solutions are posted. You should have received your final
grades. Have a wonderful summer everyone!
Handouts:
- Syllabus (pdf)
- Collaboration table (pdf)
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)
- Lecture 7: Razborov's lower
bound on monotone circuits for clique (pptx, pdf)
- Lecture 8: Schwartz-Zippel, Valiant-Vazirani Theorem, randomized complexity
classes, error reduction, BPP in P/poly, (pptx, pdf)
- Lecture 9: Goldreich-Levin hard bit, Yao's Lemma, BMY generator (pptx, pdf)
- Lecture 10: Nisan-Wigderson generator, error-correcting codes (pptx, pdf)
- Lecture 11: transforming worst-case hardness into average-case
hardness (pptx, pdf)
- Lecture 12: extractors, RL, oracles, the PH and alternating
quantifiers (pptx, pdf)
- Lecture 12.5: the PH and alternating
quantifiers, complete problems
for levels of the PH and PSPACE, Karp-Lipton Theorem, BPP in PH, the class #P,
complete problems for #P (pptx, pdf)
- Lecture 13: #Matching is #P-completes, interactive proof systems, graph non-isomorphism, the
power of IP (pptx, pdf)
- Lecture 14: IP = PSPACE, Arthur-Merlin games, the classes MA and
AM (pptx, pdf)
- Lecture 15: derandomization of MA and AM, optimization, approximation, and PCPs (pptx, pdf)
- Lecture 16: elements of the proof of the PCP Theorem (pptx, pdf)
- Lecture 17: finishing up PCPs (pptx, pdf)
- Lecture 18: relativization and natural proofs; course summary (pptx, pdf)
Problem sets:
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.