CS221 Lectures

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Lectures so far:

  • Lecture 01 (9/18): Introduction.
  • Lecture 02 (9/20): Turing Machines, Computational Problems and Complexity Measures (ps) (pdf).
  • Lecture 03(9/25) (unedited): Last Comments on Turing Machines, Time Hierarchy (doc).
  • Lecture 04 (9/27): More Hierarchy Theorems (ps) (pdf).
  • Lecture 05 (9/30): Space, Nondeterminism (ps) (pdf).
  • Lecture 06 (10/2): Nondeterminism, Nondeterministic Time Hierarchy, Relations between Resources (ps) (pdf).
  • Lecture 07 (10/4): Completeness (ps) (pdf).
  • Lecture 08 (10/7): Completeness, NL (ps) (pdf).
  • Lecture 09 (10/9): Savitch's theorem, NL=co-NL (ps) (pdf).
  • Lecture 10 (10/11): Alternation, PSPACE=AP (ps) (pdf).
  • Lecture 11 (10/16): Alternation, PSPACE, Geography is PSPACE-complete (ps) (pdf).
  • Lecture 12 (10/18): The Polynomial Hierarchy (ps) (pdf).
  • Lecture 13 (10/21): Does the Polynomial Hierarchy collapse? DTIME(n) different from NTIME(n) (ps) (pdf).
  • Lecture 14 (10/23): More on NTIME(n) =/ DTIME(n), and Provably Intractable Problems (ps) (pdf).
  • Lecture 15 (10/25): EXPSPACE completeness (ps) (pdf).
  • Lecture 16 (10/28): Recap, Relativization, Randomized Computation (ps) (pdf).
  • Lecture 17 (10/30): Randomized Complexity and Identity Testing (ps) (pdf).
  • Lecture 18 (11/4): Randomized Computation and Circuit Complexity (ps) (pdf).
  • Lecture 19 (11/6): Circuit Complexity, Threshold Function, BPP in P/Poly (ps) (pdf).
  • Lecture 20 (11/8): Existence of Functions of High Circuit Complexity, Circuit Complexity versus Uniform Complexity, Circuit Depth (ps) (pdf).
  • Lecture 21 (11/13): Circuit Depth, NC (Papadimitriou 15.5, 16.1) (ps) (pdf).
  • Lecture 22 (11/15): NC, AC (Papadimitriou 15.5, 16.1) (ps) (pdf).
  • Lecture 23 (11/18): Parity is not in AC_0 (ps) (pdf).
  • Lecture 24 (11/20): Counting Problems, #P (Papadimitriou 18) (ps) (pdf).
  • Lecture 25 (11/22): Counting, Approximate Counting (ps) (pdf).
  • Lecture 26 (11/25): Average Case Complexity, Random Self Reducibility of the Permanent (ps) (pdf).
  • Lecture 27 (11/27): Average Case Complexity, Low-Degree extensions (ps) (pdf).
  • Lecture 28 (12/02): Interactive Proof Systems, Graph Nonisomorphism. (PCMI Lecture Notes (handout), Papadimitriou 12.2) (ps) (pdf).
  • Lecture 29 (12/04): P^{#P} in IP (ps) (pdf).
  • Lecture 30 (12/06): IP=PSPACE, AM, MA (ps) (pdf).
  • Lecture 31 (12/09): Multiprover Interactive Proofs, Probabilistically Checckable Proofs (ps) (pdf).
  • Lecture 32 (12/11): The PCP theorem and its implications about hardness of approximating optimization problems (ps) (pdf).
  • Lecture 33 (12/13): Hastad's optimal PCP, more hardness of approximating optimization problems (ps) (pdf).
  • Lecture 34 (12/16): More hardness of approximation, NP in PCP[polylog,polylog] (ps) (pdf).
  • Lecture 35 (12/18): The PCP Theorem, Final Thoughts (ps) (pdf).