ineractive proof systems

CS Table (Friday, February 7, 2014): "P vs. NP"

This Friday at CS Table, we will consider the classic “P vs. NP” problem.

Fortnow, Lance. “The status of the P versus NP problem.” Communications of the ACM 52 (2009), no. 9, pp. 78–86.

In this article I look at how people have tried to solve the P versus NP problem as well as how this question has shaped so much of the research in computer science and beyond. I will look at how to handle NP-complete problems and the theory that has developed from those approaches. I show how a new type of “interactive proof systems” led to limitations of approximation algorithms and consider whether quantum computing can solve NP-complete problems (short answer: not likely). And I close by describing a new long-term project that will try to separate P from NP using algebraic-geometric techniques.

This article does not try to be totally accurate or complete either technically or historically, but rather informally describes the P versus NP problem and the major directions in computer science inspired by this question over the past several decades.

Computer Science Table is an open weekly meeting of Grinnell College community members (students, faculty, staff, etc.) interested in discussing topics related to computing and computer science.

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