#
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).