COMPSCI 741: Complexity Theory

David Mix Barrington

Fall, 2019

This is the homework index page for CMPSCI 741. CMPSCI 741 is an advanced graduate course in computational complexity theory, with a focus on circuit complexity and its connections to automata theory and logic. The exact subject matter treated will depend somewhat on the interests of the students.

• Homework #1, Due Thu 19 September: Do the following problems in the PCMI Basic lecture notes: B1 #10, B2 #2, B3 #4, B4 #5, B5 #4, B6 #4, and B7 #3.
• Homework #2, Due Thu 9 October:: Do the following problems in the PCMI Basic lecture notes:
  • B8 #3: Show completeness under log-time uniform AC⁰ reductions.
  • B9 #4 and #5
  • B10 #7
  • B11 #1 and #11, but for #11 you should prove instead something that is true: A language has an ATM game with O(log n) time and O(1) alternations iff it is in DLOGTIME-uniform AC⁰.
  • B12 #10
  • B13 #4 and #8
  • B14 #5
• Homework #2, Due Tue 19 November:: Do the following problems in the PCMI Advanced lecture notes:
  • A1 #6
  • A2 #4
  • A3 #6 and #7
  • A4 #3 and #4
  • A5 #4 and #7
  • A6 #5
  • A7 #1, #5, and #6 (the last is optional)

Last modified 31 October 2019