P != NP

P=NP = P=NP(^2)

Verifying if I have a gf = P
Finding a gf = NP hard

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P=NP
N=1 || P=0
P!=NP

But you're right.

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Technically speaking, every boolean problem is a probability problem, just with probabilities of 0 and 1. P=NP is a problem where the only useful answers are 0 and 1. If we don't have a polynomial time solution to an NP problem, then whether you think the probability that P=NP is 0.5 or 0.7 or 0.3 doesn't really matter. It's still as if P != NP, and we have to keep searching, or prove the probability is 0. If we do find such a problem, then the probability that P=NP is 1.

Has nothing to do with P=NP. This is a complexity class problem, not a decidability problem.

>complexity
how you can estimate complexity if cannot even estimate termination?

Complexity classes of algorithms are proven by humans, not by turing machines. We don't have a general procedure for proving the complexity class of all possible algorithms as well. In general, any algorithm that has a possibility to not terminate on any input is O(∞)

human is turing complite, not any more
en.wikipedia.org/wiki/Turing_completeness#Examples

This link does not show any proof or link to any proof suggesting that the human brain reducible to a turing machine.

(You)r brain it some low power useless black box
all inelegense of humanity writen on some formal langiage in books
all known formal langiages just turing complite

Took 21 replies to reach full shitposting

even if (You)r brain superior over turing mashine have no way to share this power with another human

0=1

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Took one post to verify, hence, P!=NP

If there is one problem that is P and NPC then P=NP

also assumed N =/= 1

This.
1 = 0.999...
0.000...1 = 0.000...0
1 = 0

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P! = 1 ... (P-1) P = NP
=> N = (P-1)!

>terminating decimal is the same thing as non-terminating decimal
I see you graduated from Poo-U with a degree in computer science

math major detected
you'll have 40+ years of your hs teacher career to get worked up about dumb jokes so save some for later

Quod
Erat
D-d-d-die nigga

No human has ever performed a computation that could not be done on a turing machine running a clever program.

What happens when P=0?

Can a Turing Machine write a symphony?

Unknown but probably yes.
The problem is there's no clear definition of what a symphony is.

P!=NP

Then
P=NP
P - NP = 0
P(1 - N) = 0

P = 0

1 - N = 0
N = 1

0!=1*0
0!=0
False

So
P=NP
Q.E.D.

>It's clearly easier to prove P!=NP than P=NP
No. If you want to prove P=NP all you need to do is provide a polynomial time algorithm for an NP-complete problem. If you want to prove P!=NP you have to prove that no polynomial time algorithm for an NP-complete problem exists. The latter is much harder to prove because you have to completely rule out any possibility of a polynomial time algorithm including roundabout solutions using deep mathematical insights that have not been discovered yet.

Yes. Music generation AI exists and does a pretty good job. Plus, there is nothing special about a symphony at all. You enjoy them because it's an ordered and structured sequence of sound that pokes at "this is aesthetic and nice" buttons in your brain? Why does it do that? Because another human made it, and they optimized their work to effectively push those pleasure buttons.

Writing a symphony is a quite low bar for a machine. You might as well have asked "can a turing machine analyze arbitrary objects in a scene as well as a human can". The answer is still yes. We know it is, but we're a lot further away from a solution to that problem.

Please ignore the stray question mark on "brain?"

You're probably wrong.

So basically solving sudoku in polynomial time would be enough to prove P=NP? Next Jow Forums project? I'll make the logo

You're probably one of those brainlets who believe the halting problem means a machine can never tell whether a particular algorithm will halt or not.

>humans cannot be reduced to Turing machines
Spotted another brainlet.

Just make one that outputs every possible valid arrangement of musical notes, or one that creates every possible audio file.

>Qouted es drue

>You're probably one of those brainlets who believe the halting problem means a machine can never tell whether a particular algorithm will halt or not.
at start do solve problem:
1. it some_programm is NP, P or not
2. for this(1.) sollution need to know some_programm will halt or not
and this (2.) is imposible cose en.wikipedia.org/wiki/Halting_problem

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also in P != NP problemm deffination
used S(n) asimtomatic difficulty deffination
it mean P and NP problems muast be infinity scalable from n
enctypting algoritmas is not scalable
------------------
alls this CS shit is just bullshit

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Do you genuinely believe it's more likely that such a trivial proof of the P vs NP problem being unsolvable has eluded mathematicians and computer scientists all this time than that you simply misunderstood the problem? The answer is no, because you're just a shitposter.

>eluded mathematicians and computer scientists
they evil or retarded

anyway S(n) asimtomatic difficulty deffination it avalable for very small amout of all programms

Maybe we should prove that it is impossible to prove instead

CS not formal enought
cose formalisation will revelal how shity and useless all this shit

Yes. However, if P!=NP, you will never find a polynomial time algorithm for sudoku.

He's trying to prove that assumption. That's not uncommon. He's also dividing 0 in his proof. That's not uncommon proving bullshit too.

This is actually a madad proof.
The solution to the top line is either p=0 or n=1. On the 4th line, he divides by n-1. If it was the n-1 case, this would not be possible, so he ends up showing the p=0 case.

This is how you prove things, he didn't do anything right, but you can prove things like that by contradiction - assume a thing and show it is logically inconsistent ifyou assume it - > that thing isn't true since it leads to contradiction