Honors Theory of Computation, Spring 2002
LINKS and INFORMATION

• Feb 7, Talk at CUNY Graduate Center by Juris Hartmanis on "P versus NP, Revisited"

  	Juris Hartmanis
  	Department of Computer Science, Cornell University
  
  	Thursday, February 7, 2002
  	4:00 p.m.,  Room 9204
  	CUNY Graduate School
  	365 Fifth Avenue, NYC
  
  
  Abstract:
  The P versus NP problem is the best known unsolved problem in theoretical
  computer science with deep implications about the limits of feasible
  computations and the nature of mathematics. Its solution will be rewarded
  by a million dollar prize from the Clay Foundation which ranks it among the
  seven most important open problems in mathematics.  More important, its
  solution will be a major step towards understanding what is feasibly
  computable and, indirectly, the limits of feasible rational reasoning.  The
  solution will also clarify how much harder is it to compute a proof of a
  theorem than to check the correctness of a proof.
  
  At the same time, the P versus NP question is only one of many other
  important "separation" problems of the rich structure of natural complexity
  classes below exponential space. We "know" that these complexity classes
  must all be different, but there are no proofs (yet) to support this
  belief.
  This talk will revisit the P versus NP problem in this broader setting,
  review the attempts to solve the separation problems,explore connections
  between these problems, and review their relation to descriptive
  complexity, oracle computations, and interactive proofs.
  
  For further information, please contact Professor Sergei Artemov
  sartemov@gc.cuny.edu
  

• Talk at Courant/NYU by Peter Shor ``Quantum Algorithms'' on Mon Feb 4th
  Time 3:30 to 4:45 in WWH 109 (refreshments in the lounge before the talk).
  ABSTRACT: Quantum computers are hypothetical devices which use the principles of quantum mechanics to perform computations. For some difficult computational problems, including the cryptographically important problems of prime factorization and finding discrete logarithms, the best algorithms known for classical computers are exponentially slower than the algorithms known for quantum com- puters. Although they ave not yet been built, quantum computers do not appear to violate any fundamental properties of physics. I give a mathematical model of quantum computation, explain how quantum mechanics provides this extra computational power, and briefly describe the algorithm for efficient prime factorization.