Because we don’t know whether equal is equal, what we need to prove is equal is not equal.
To put it simply, the computer solves different problems by breaking them into the most basic operations such as addition, addition, subtraction and so on.
So how difficult a question is... Well, mainly how difficult it is for a computer depends on how many steps it can be divided into, or how much time it takes - the time for basic computer operations is basically the same, so ignoring the space factor,
The two are roughly equivalent.
This is called time complexity, represented by Big O, also called asymptotic notation.
O(1) is the constant level complexity - the most common calculation, as the data size increases, the calculation time will also increase.
O(logn) is a little more complicated.
Then there are O(n), O(nlogn), O(n^), O(n!), O(n^n)...
Level by level, the difficulty increases step by step, and the time taken to solve the problem skyrockets.
Among them, it can be solved in polynomial time under O(n^c), which is called a P-type problem.
Above this, although there will be exponential or even more extreme surges as n increases, they have one thing in common, that is, the forward solution is difficult. It is generally not difficult to give you an answer to verify.
For example, prime factorization of large numbers.
It is difficult to know whether a large number is prime. You need to start from 2 and divide it all the way to the root n.
But if I tell you that it is divisible by a certain number, it only takes a few steps to verify it.
This type of problem that can be verified in polynomial time is called an NP problem.
Obviously, all P-type problems are NP problems because they are simple and verifiable.
But are NP-type problems all P-type problems? Are there some special algorithms that can reduce the difficulty of these problems to the point where they can be solved in polynomial time, as if the answers can be verified?
This is "P=NP?".
During the research process, another NPP-hard problem emerged.
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.
[I won’t talk about NP-hard. This is a type of problem including NPPC. The definition is beyond NP, so it has nothing to do with this question. ]
At first, everyone thought that NPC was just a fantasy, until such a problem really arose.
That is the origin of NPC - logic circuit problem.
Since then, a lot of NPCs have appeared, because to prove new NPCs, all we need to do is reduce them to known NPCs. So the Hamiltonian cycle, the TSP problem, the SAT problem, the knapsack problem, and the traveling salesman problem all became
NPC.
But the person who asked this question must not have seen Ye Han’s paper on protein folding...
Or you saw it and haven’t had time to change it;
You may also want to change but have no regrets and cannot change...
If P=NP is proved, then the whole world will become completely different from what we think.
Inspiration and creativity will have no value, because the solutions to all problems can be solved using hard-working algorithms and in polynomial time.
It is as if anyone who can appreciate a symphony can become Mozart; anyone who understands mathematical argumentation can be Gauss; anyone who studies investment strategies can be Buffett...
By the same token, predicting protein folding no longer requires exhaustive methods; a definite answer can be obtained in polynomial time.
How can it be!
Therefore, regarding the problem of P=NP?, Ye Han is inclined to the majority opinion in the industry - it is not tenable.
However, he has not been able to successfully prove or falsify, but just proposed that a certain type of NPPC problem is not equivalent - this is already very powerful.
What's more powerful is that he developed a chaos model for this type of problem and gave the corresponding three-dimensional manifold attractor, referred to as the Ye's attractor, and then combined it with a certain space tiling algorithm to make substantial optimization and corrections.
Most people know the theory of relativity and quantum mechanics, and have heard the word chaos, but they may not necessarily know that chaos theory, alongside quantum mechanics and relativity, is considered the greatest discovery in the scientific field of the 20th century.
Many people say that there has been no decent progress in physics for more than a hundred years, and the discovery of chaos is definitely one of them.
From the three-body problem, to turbulence, to molecular thermal motion...including biological populations and astronomical research, the shadow of chaos is everywhere.
Although it is still difficult to give an exact answer, after all, it is difficult to have an exact answer to the chaos problem, otherwise it would not be called chaos.
However, it can be regarded as a success in providing an optimization algorithm for solving this type of problem in polynomial time.
Fortunately, among the questions given by Yonemura, there was one in the series that he solved.
Although it seems to have nothing to do with protein folding on the surface, in fact, as long as the reduction is proved, it can be simply copied and pasted...
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Do we need to provide proof?
Because if you give it, it will inevitably be seen. Even though it has been published, hasn’t it been recycled again?
Ye Han asked for confirmation: "There is definitely no problem with my proof, but... are you sure that the person who asked the question can understand my proof?"
This is not funny at all.
Could the Greeks who raised the problem that the three rulers and compasses could not be used to construct drawings understand the proofs of Vanzil and Lindemann?
Do Italian Tartaglia and Cardano understand Gavarro's group theory?
Even Fermat, could he understand Andrew Wiles's 130-page paper?
The person who asked the question did not understand how difficult the question he was asking was, which is common in the world of mathematics.
It can even be said that every famous conjecture has the same problem - if the conjecture is not old enough and does not live long enough, it will definitely not be famous or impressive.
And as long as it is awesome, the proof process must be extremely complicated, and it is almost impossible for the person who asked the question to understand it.
Ye Han's paper was approved after months of peer review.
No matter how powerful the Americans are, Ye Han feels that it is extremely difficult to gather the number of colleagues who are qualified to review him. The probability of not having one is far greater than that of having one.
Why?
If there were, then research on the nature of the universe, quantum mechanics, and the theory of everything should have made some progress long ago. Even if Huaxia Village did not participate, they should have heard about it, but they did not.
If there were, the issue of guarding would probably not be so old-fashioned and misleading; the strategies for foreign villages would not be so closed-minded, conservative and unconfident...
[Oh, they gave several sets of parameters. You substitute the parameters into the solution. As long as the answer given within the specified time is correct, that's it. 】
Sure enough... Ye Han couldn't help but push his eyes.
Although NPC problems do not have the best solution within a polynomial, there are many approximation algorithms, such as greedy algorithms, divide and conquer algorithms, dynamic programming algorithms, genetic algorithms...
The verification solutions given by this group of people, in all likelihood, as long as the algorithm is correct, it will be considered correct even though it is obviously incorrect.
In fact, his algorithm is also an approximation algorithm, but it can achieve the required accuracy at any given scale, which is completely different from those rough and low-pitched algorithms.
"I can guarantee that my algorithm is accurate enough, but I cannot guarantee that the solutions given by those people are correct enough..."
He couldn't understand the paper, so he had to rely on black box testing. He showed his cowardice in this way, and Ye Han was not optimistic about the answers given by these people.
During exams, isn’t it rare that the examiner gives the wrong answer?
With that said, he asked the system for parameters and began to enter them for verification.
It was a bit surprising. Although many of these seven or eight sets of parameter data were long in digits and extremely complex, the answers given by the other party were completely correct.
So, go through it again!
Ye Han's body began to sparkle!
【(づ￣3￣)づ…………】
Go to bed, go to bed, go to bed, go to bed! This guy really did it!