What is "P=NP? "Question," "That's the key.

Because I don't know if waiting is not equal, what needs to be proved is whether waiting is not equal.

To put it simply, the computer solves different problems by splitting them into the most basic operations such as addition, subtraction, and subtraction.

So how difficult is a question...... Well, it's mainly about how difficult it is for a computer, depending on how many steps it can be broken down, or how much time it takes - the time for basic computer operations is basically the same, so ignoring the spatial factor, the two are roughly equivalent.

This is called time complexity, and it is represented by the big O or the progressive symbol.

O(1) is the constant-level complexity - the most conventional calculation, the amount of data size increases, and the time spent on the operation also increases.

O(logn) is a bit more complicated.

And then there are O(n), O(nlogn), O(n^), O(n! ），O（n^n）……

Level by level, the difficulty rises layer by layer, and the time taken to solve the problem skyrockets.

where O(n^c) is solved in polynomial time, which is called a P-class problem.

On top of this, although there will be an exponential or even more excessive surge with the growth of n, there is one thing in common, that is, the positive solution is difficult, and it is generally not difficult to give you an answer to verify.

For example, the prime factor decomposition of large numbers.

It is difficult to know if a large number is prime, you need to start with 2 and divide until n is under the root.

But to tell you that it is divisible by a certain number, you can verify it, it is only a matter of a few steps.

This kind of problem, which can be verified in polynomial time, is called an NP problem.

Obviously, all P problems are NP problems because they are simple and verifiable.

But are all NP questions P? Is there some special algorithm that reduces the difficulty of these problems to the point where polynomial time can be solved, as if the answers were verified?

This is what "P=NP?" "That's it.

In the process of research, the NPP-hard problem was born.

The so-called NPP problem can be reduced to a type of problem.

As long as such a problem is solved, a large number of problems can be solved incidentally. As long as it is proved that there is a fast algorithm for the NPC problem, it is basically proved that P=NP.

[NP-hard aside, this is a type of problem that includes NPPC, and the definition is beyond NP, so it has nothing to do with this question.] 】

At first, everyone thought that NPCs were just a pipe dream, until such a problem actually appeared

That is, the originator of NPCs - logic circuit problems.

After that, a whole bunch of NPCs popped up, because to prove a new NPC, all you had to do was reduce it to a known NPC, so the Hamiltonian loop, the TSP problem, the SAT problem, the backpack problem, the traveling salesman problem, all became NPCs.

However, the person who came up with this question must not have seen Ye Han's paper on protein folding......

Or I saw it and didn't have time to change it;

You may also want to change it, but you have no regrets, and you can't change it......

If P=NP is proven, the whole world will be completely different from what we think it is.

Inspiration and creativity will be of no value, because the solution of all problems can be solved with an algorithm of effort, and in polynomial time.

It's as if anyone who can appreciate a symphony can become Mozart; Everyone who knows how to argue mathematically is Gauss; Everyone who studies investment strategies can be Warren Buffett......

By the same token, predicting protein folding is no longer exhaustive, and polynomial time can be used to determine the answer.

How can it be!

So for P=NP? Question, Ye Han is inclined to the majority opinion of the industry - not true.

However, he was not able to prove or falsify it either, but only raised the question that a certain type of NPPC problem is not equivalent – which is already powerful.

What's more powerful is that he made a chaotic model of this kind of problem, and gave the corresponding three-dimensional manifold attractor, referred to as Ye's attractor, and then combined with a certain spatial dense paving algorithm, it was greatly optimized and corrected.

Most people know the theory of relativity, know quantum mechanics, and have heard the word chaos, but they don't necessarily know that chaos theory, along with quantum mechanics and relativity, is considered the greatest discovery in the field of science in the twentieth century.

Many people say that physics has not made decent progress for more than a hundred years, and the discovery of chaos is definitely one.

From the three-body problem, to turbulence, to molecular thermal motion...... Including biological populations, astronomical research, there is no shadow of chaos everywhere.

Although it is still difficult to give a definite answer, after all, it is difficult to have a definite answer to the problem of chaos, otherwise it would not be called chaos.

However, it can be regarded as a successful optimization algorithm for solving this type of problem type in polynomial time.

Very lucky, one of the problems given by Yonemura belongs to the series that he solved.

Although it seems to have nothing to do with protein folding, in fact, as long as it is proved to be reduced, it can be simply copied and pasted......

==========

Do you want to prove it?

Because it was given, it was inevitably seen, and although it was published, wasn't it recycled?

Ye Han asked confirmatively: "I definitely have no problem with this proof, but ...... Are you sure that the person who asked the question can read my proof? ”

It's not funny at all.

Can the Greeks, who raised the question of the impossibility of drawing the three rulers, understand the proof of Wanzhil and Lindemann?

Can Italy's Tartaglia and Cardano understand Gavaro's group theory?

Even Fermat, can you read Andrew Wiles' 130-page paper?

It is not uncommon in mathematics for people who ask questions to understand how difficult their questions are.

It can even be said that every famous conjecture has the same problem - the conjecture is not old enough and does not live long enough, then it is definitely not famous and not bullish.

As long as it is awesome, the proof process must be extremely complicated, and it is almost impossible for the questioner to understand.

Ye Han's paper was approved, but it was peer-reviewed for several months.

No matter how strong the people of the United States are, Ye Han feels that it is extremely difficult to gather the number of peers who are qualified to evaluate him. Even the probability of not having one is far greater than having one.

Why?

If there were, then the research on the nature of the universe, as well as quantum mechanics and the theory of all things, should have made some progress a long time ago.

If there is, most of the topics will not be so old-fashioned; The strategy of the outer village will not be so closed, conservative and unconfident......

[Oh, they give several sets of parameters, you substitute the parameters into the solution, as long as the answer given within the specified time is correct, it's fine.] 】

Really...... Ye Han couldn't help but push his eyes.

Although there is no optimal solution to the NPC problem in polynomials, there are many approximation algorithms, such as greedy algorithms, divide and conquer algorithms, dynamic programming algorithms, and genetic algorithms......

The verification solution given by these people, as long as the algorithm is correct, it will be considered correct even if it is wrong.

In fact, his algorithm is also an approximation algorithm, but it can achieve the required accuracy at any given scale, which is not at the same level as those rough and low-beeping algorithms.

"I can guarantee that my algorithm is accurate enough, but I can't guarantee that the solution given by those people is correct enough......"

If you can't read the paper, you have to rely on the black box test, so timid, Ye Han is not optimistic about the answers given by these people.

When it comes to exams, isn't it rare for the questioner to give the wrong answer?

With that, he asked the system for parameters and began to verify it.

It was a bit surprising that although many of the seven or eight sets of parameter data were very long and extremely complex, the answer given by the other party turned out to be completely correct.

So, over and over again!

Ye Han's body began to shine!

【（づ￣3￣）づ…………】

Lie to lie to lie to lie to sleep! This guy really made it!