Hacker News Reader

What would really be interesting is someone finding a nonconstructive proof that P = NP. It would be quite a scramble to find the missing algorithms...

View on HN

We already have algorithms for all NP problems, by Levin. See: http://en.wikipedia.org/wiki/P_versus_NP_problem#Polynomial-...

No one knows whether it runs in polynomial time though! It runs in polytime if P=NP.

"// "Polynomial-time" means it returns "yes" in polynomial time when // the answer should be "yes", and runs forever when it is "no"."

That's an odd definition of polynomial time.

It is just a technicality. If you know an upper bound on the running time you can simply run it for that many time steps and then return "no" if it doesn't halt by then (because it could never thereon answer "yes"). This only works with concrete upper bounds on running time (and not for general decidability).

Reply on news.ycombinator.com