CS 151: Complexity Theory (Spring 2019)

Instructor: Chris Umans

Office: Annenberg 311

Times: Tu/Th 1:00-2:25 in Annenberg 314

TAs: Andrew Ding, Gideon Leeper, and Siddharth Prasad

Office hours:

• Tuesdays 7-8pm in Annenberg 106 (Siddharth)
• Wednesdays 2-3pm in Annenberg 311 (Chris)
• Wednesdays 4-5pm in Annenberg 106 (Andrew)
• Wednesdays 7-8pm in Annenberg 106 (Gideon)

Announcements:

• All solutions are posted. Graded material can be picked up from me. Have a great summer!!

Handouts:

• Syllabus (pdf)
• Collaboration table (pdf)

Lecture slides:

• Lecture 1: intro; languages, complexity classes, Turing Machines, reductions and completeness (pptx, pdf)
• Lecture 2: time and space classes, hierarchy theorems, relationships between classes, padding (pptx, pdf)
• Lecture 3: padding and succinctness, nondeterminism, NP- and NEXP- complete problems, NTIME hierarchy theorem, Ladner's Theorem (pptx, pdf)
• Lecture 4: unary languages and NP, nondeterministic space classes, STCONN, Savitch's Theorem, I-S Theorem (pptx, pdf)
• Lecture 5: nonuniformity and advice, NC hierarchy (pptx, pdf)
• Lecture 6: formula lower bound on Andreev function, Razborov's lower bound on monotone circuits for clique (pptx, pdf)
• Lecture 7: Schwartz-Zippel, Valiant-Vazirani Theorem, randomized complexity classes, error reduction (pptx, pdf)
• Lecture 8: BPP in P/poly, Goldreich-Levin hard bit, Yao's Lemma, BMY generator (pptx, pdf)
• Lecture 9: Nisan-Wigderson generator, error-correcting codes, transforming worst-case hardness into average-case hardness (pptx, pdf)
• Lecture 10: transforming worst-case hardness into average-case hardness, extractors (pptx, pdf)
• Lecture 11: RL, oracles, the PH and alternating quantifiers, complete problems for levels of the PH and PSPACE (pptx, pdf)
• Lecture 12: 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, derandomization of MA and AM (pptx, pdf)
• Lecture 15: optimization, approximation, and PCPs, elements of the proof of the PCP Theorem (pptx, pdf)
• Lecture 16: finishing up PCPs (pptx, pdf)
• Lecture 17: relativization, natural proofs, course summary (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) Solutions (pdf)
• Problem Set 4: (pdf, LaTeX source) Solutions (pdf)
• Midterm: (pdf, LaTeX source) Solutions (pdf)
• Problem Set 5: (pdf, LaTeX source) Solutions (pdf)
• Problem Set 6: (pdf, LaTeX source) Solutions (pdf)
• Problem Set 7: (pdf, LaTeX source) Solutions (pdf)
• Final: (pdf, LaTeX source) Solutions (pdf)

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.