Math 267AB - Circuit Complexity

Instructor: Sam Buss
U.C. San Diego, Winter-Spring 1992

Student-written scribe notes and homework problems are available in PDF and postscript format.

Topics covered:

  1. Shannon and Lupanov theorems.  Scribe: Bob Carragher.

  2. Spira and Krapchenko theorems.  Scribe: Matt Clegg.

  3. Neciporuk's theorem, simulation of Turing machines by circuits.  Scribe: Frank Baeuerle.

  4. AC, NC, CVP, space bounded TM's, Addition in NC1Scribe: John Lillis.

  5. Parallel Prefix, Symmetric functions. Scribe: Goran Gogic.

  6. Schnorr and Blum lower bounds. Scribe: Dave Robinson.

  7. Subbotovskaya's and Andreev's lower bounds.  Scribe: Jinghui Yang.

  8. Hastad's Switching lemma.  Scribe: Elias Koutsoupias.

  9. Applications of Hastad's lemma. Scribe: Sam Buss

  10. Constant-depth reducibility (Chandra-Stockmeyer-Vishkin), Smolensky's theorem, part 1.  Scribe: Frank Baeuerle.

  11. Smolensky's theorem, part 2, Probabilistic circuits.  Valiant-Vazirani theorem, part 1. Scribe: Goran Gogic.

  12. Valiant-Vazirani theorem, part 2, theorems of Toda and Allender-Hertrampf, Scribe: Jinghhui Yang.

  13. Uniformity, unbounded and bounded fanin.  Scribe: Dave Robinson.

  14. Uniformity of AC0, linear time hierarchy, multiplication and division (Beame-Cook-Hoover).  Scribe: Elias Koutsoupias.

  15. Low-depth circuits for division, continued.  Scribe: Sam Buss

  16. Unified list of homework assignment.