CS 278 -- Computational Complexity

All lecture notes in a single ps file

  [links] [notes]

People

• Kurt Godel
• Alan Turing

P, NP, and all that stuff

• M. Sipser. The History and Status of the P versus NP question

Contains the now-famous letter of Godel to von Neumann
• C.H. Papadimitriou. NP-completeness: a retrospective.
• O. Goldreich. Computational Complexity

On the nature of complexity-theoretic results
 

• Once more, we have decreased the number of open questions in the field - without, alas, increasing much the number of answers!

(C.H. Papadimitriou and M. Yannakakis, "Optimization, Approximation, and Complexity Classes." JCSS 43:425-440, 1991.)

• I do believe it

Against an oracle
(Line spoken by Fernando in "The Tempest," by William Shakespeare)
• This is as strange a maze as e'er men trod

And there is in this business more than nature
Was ever conduct of: some oracle
Must rectify our knowledge
(Line spoken by Alonso in "The Tempest," by William Shakespeare)

• This administration is doing everything we can to end the stalemate in an efficient way. We're making the right decisions to bring the solution to an end.

(President G.W. Bush, April 10, 2001)

Lecture Notes

• [Lecture 1] (preliminary version posted 1/21) decision problems, search problems, P, NP, reductions, NP-completeness
• [Lecture 2] (preliminary version posted 1/23) NP-completeness of SAT and 3SAT
• [Lecture 3] (posted 1/28) NP-completeness of Independent Set, introduction to space-bounded classes.
• [Lecture 4] (posted 2/12) NL-completeness, Savitch
• [Lecture 5] (posted 2/12) NL=coNL, polynomial hierarchy
• [Lecture 6] (posted 2/12) Circuits
• [Lecture 7] (posted 3/18) Probabilistic complexity classes
• [Lecture 8] (posted 3/18) Probabilistic algorithms
• [Lecture 9] (posted 3/18) BPP versus PH, and counting problems
• [Lecture 10] (posted 3/18) Approximate counting
• [Lecture 11] (posted 3/18) Valiant-Vazirani, introduction to cryptography
• [Lecture 12] (posted 3/18) One-way function, hard-core predicates, pseudorandom generators
• [Lecture 13] (posted 4/5) Pseudorandom generators, pseudorandom functions
• [Lecture 14] (posted 4/5)Error-correcting codes and Goldreich-Levin
• [Lecture 15] (posted 5/2) Levin's average-case complexity theory
• [Lecture 16] (posted 4/5) Average-case complexity of the permanent
• [Lecture 17] (posted 5/2) Introduction to interactive proofs
• [Lecture 18] (posted 5/2) IP=PSPACE
• [Lecture 19] (posted 5/2) IP=PSPACE
• [Lecture 20] (posted 5/2) PCP and hardness of approximation
• [Lecture 21] (posted 6/12) NP=PCP[log n, polylog n]
• [Lecture 22] (posted 6/12) NP=PCP[log n, polylog n]
• [Lecture 23] (posted 5/2) parallelization
• [Lecture 24] (posted 6/12) parallelization
• [Lecture 25] (posted 6/12) NP in PCP[poly(n),O(1)] (april 20)
• [Lecture 26] (posted 6/12) Pseudorandomness and derandomization (april 23)
• [Lecture 27] (posted 6/12) Nisan-Wigderson (april 25)
• [Lecture 28] (posted 6/12) Extractors (april 30)
• [Lecture 29] (posted 6/12) Extractors, error-correcting codes, and worst-case to average-case reductions (May 2)
• [Lecture 30] (posted 6/12) Miltersen-Vinodchandran (may 7)