What would happen if P=PN?

The painting analogy is pop-sci bullshit.

These kind of statements are retarded.

Just the fact that there's a polynomial-time solution to a problem doesn't mean that it isn't O(n^(weight of your mother))

There's nothing wrong with it if we're assuming the human brain has access to the algorithm that reduces NP to P.

or that the constant suppressed by the big-O notation isn't larger than the number of atoms in the universe

It assumes a well-defined algorithm for valuing art and making valuable art, which is in no sense necessarily true. It's just hand-wavy bullshit you use when you're explaining shit to plebs.

P does equal NP, you will find this out when the singularity occurs in 2026

>Because P = NP means that being able to verify a solution to a problem is the same as finding a solution to that problem.

This is more about NP-complete and NP-hard

P=NP is an intellectual pursuit.

Quantum Computers theoretically can solve NP-Complete problems in polynomial time.

P=NP? is based on a strict environment which constrains how you solve the problem.

it would be extremely painful

tep kok

>le encryption is broken pop sci meme

This guy gets it

If in the future we find P=NP, it would mean that P=NP is true right now... and we're doing okay. It could just end up meaning, people will know there are polynomial solutions to certain problems with no clue what the solutions are... just that they exist.

>all

Try again.

wrong! it wouldnt be millenium problem otherwise, there is also the possibility that P=infinity and N=2 for example.

Really? Will the next logical question be, does P=NP-hard?

>le brainlet

ur iPhone would become much easier to crack

not an argument

>It's another interpreting P vs NP as an algebraic equation episode

>Quantum Computers theoretically can solve NP-Complete problems in polynomial time.
No they can't.

If a quantum algorithm emerged that could solve an NP complete problem in P time then everyone in the field would completely lose their fkn shit.

an algorithm that can be solved in a polynomial time using a quantum computer would substitute an entire different complexity class
BQP (bounded-error quantum polynomial time)
this has nothing to do w/ either P or NP
it's actually an analogue of BPP (bounded-error probabilistic polynomial time) for quantum computers

Not if the proof is constructive. Which it probably won't be, but whatever.

>non-constructive proof that P = NP
the dream

got a problem you want to know such as a) should I go to college and make money or b) do something else to make money

if p = np you will know the answer without spending 4 years at uni while also not googling how to make money elsewhere/elsehow

it basically optimizes anything you want to know

>PN
It's not commutative

>It's not commutative
Good luck teaching someone who only knows algebra how mathematical theory works, boss.

Why wouldnt it (apart from the P being not equal to NP)

here is a better one
>What would happen if P=EXPTIME?

non-polynomial time = NP
polynomial-non time = PN

what did he mean by this?

>NP stands for non-polynomial
REEEEEEEEEEEEEEEEEEEEE

>non-polynomial
ah fuck me I meant nondeterminist

You're a big brainlet.

If P is 0 then N can be 1 which means it's just a binary computer science theory, moron.

you're not worth arguing with

You retard

So encryption not being useless at this moment is a proof that P is in fact not equal to NP?

No, it may mean that we just fail to see the otherwise obvious shortcuts, until the formal proof of P != NP is found.

We do not know whether what we claim to be impossible (meaning elapsing infinetely/unimaginably long time to solve) really is impossible.

There may very well be a way to bypass all modern encryption, that we just fail to see, until the P?NP problem is definitely resolved.

>He thinks a bank's security network is full of mathematicians that can be bypassed using a better mathematician

This isn't Swordfish, Pajeet. Go back home.

It will never be proven, Wojack. Go back to sleep.

Most encryption being broken isn't a meme. The stupid painting analogy is, but encryption breaking is the real thing. Most encryption schemes are based on problems which are NP complete without the necissary passwords.

If that were true, I think perfect AI opponents for chess and go and more complicated games become easy to program.

Have you even studied modern encryption? That really is how it works.

This.
P is either equal to NP or it's not.
The question is whether humans find out about it and then use that knowledge in an efficient way.
Also, your bank's encryption probably relies on RSA, and its security relies on the difficulty of prime factorization.
Now, there are already algorithms that can solve prime factorization, and they are in P. Yet RSA is still secure.

The problem is that all problems that are NP-Complete, including factorization, can be transformed without loss of solution space via polynomial time reductions to every other NP-Complete problem.

If even one NP-Complete problem can be done in polynomial time, we would just transform all NP-Complete problems to that easy problem and solve.

If a constructive proof of P=NP exists, we don't have to know how to sove each specific NP-Complete problem. We just use the reduction proofs to transform to the one we can solve.

>P=PN
This would mean that all Petri nets are polymonially sovable and vice versa.