How important is the problem of whether or not P=NP?
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How important is the problem of whether or not P=NP?

'The question of whether P=NP has been occupying researchers since these two sets were first defined, having become the greatest unsolved problem in computer science...'
from Alan Turing: Life and Legacy of a Great Thinker

How important is the problem of whether or not P=NP?
'Does P = NP? This is undoubtedly the most profound question in computer science...'
from: Tutorial: Does P = NP?

How important is the problem of whether or not P=NP?

'The relationship between the complexity classes P and NP is an unsolved question in theoretical computer science. It is considered to be the most important problem in the field...'
from Wikipedia Article on 'P=NP' problem

How important is the problem of whether or not P=NP?

[If you can show that P=NP, then] 'most cryptographic algorithms are basically useless'
from comment by Charles on November 15, 2008 06:13 PM

How important is the problem of whether or not P=NP?

'The Clay Mathematics Institute has offered a $1 million US prize for the first correct proof.'
from Wikipedia Article on 'P=NP' problem

OMFG! They offered what!?

'The Clay Mathematics Institute has offered a $1 million US prize for the first correct proof.'
from Wikipedia Article on 'P=NP' problem

I thought that was what you said.

One MILLION dollars!

Problems sure can't get any more profound than that!

one MILLION dollars!





'jervis' on Fri, 21 Nov 2008 12:26:51 GMT, sez:

Dude!
You're missing a great opportunity.

Post this problem on mechanical turk:
------
Wanted: Proof that P=NP.
I will pay: $999,000
------
(That's a profit of $1000 in your pocket, just for typing a couple dozen words!)



'nobody' on Fri, 21 Nov 2008 14:59:20 GMT, sez:

i really just wanted to comment because the spam-filter word was "meatbag". guess that backfired.



'Alexey Romanov' on Sat, 22 Nov 2008 06:52:41 GMT, sez:

Of course you probably know it, but "[If you can show that P=NP, then] 'most cryptographic algorithms are basically useless'" is wrong.



'lb' on Wed, 26 Nov 2008 10:32:55 GMT, sez:

It reminds me of this quote from Sneakers:

"There isn't a government on this planet that wouldn't kill us all for that thing."



'Scott' on Thu, 27 Nov 2008 21:43:00 GMT, sez:

Coincidences freak me out: you post this random thought, and the same week P=NP is the subject of the evening for the Mathematical Algorithms module at uni.

Unfortunately it is not as simple as setting N=1. Bummer. I might actually have to learn something.



'lb' on Fri, 28 Nov 2008 01:01:58 GMT, sez:

>Unfortunately it is not as simple as setting N=1

or P=0. ;-)

I keep thinking about P=NP at inopportune moments, and wonder why there isn't some case P!=NP can be proved by having a really small problem domain where it can be completed shown that every combination must be considered before a solution is found.




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