P=NP? Conjecture this millennial puzzle is at the core of the field of computer mathematics.

The entire problem can be split into N secondary problems, and four of them are the most famous.

They are the problem of factor decomposition of Dazheng integers, graph isomorphism, discrete logarithmic problem, and Manhattan network problem.

Among them, the large number decomposition problem and graph isomorphism problem are the most famous because the solution to these two problems involves many basic problems in cryptography and complexity theory.

Solving them can greatly promote the development of computer science, algorithms, etc.

Not to mention the rest, just like intelligent driving, environment perception and decision-making algorithms are the key to autonomous vehicles achieving intelligent driving.

The environment perception algorithm uses on-board sensors and cameras to obtain information such as roads, obstacles, traffic signs, etc., and performs perception and modeling.

The decision-making algorithms make driving path planning, communication and coordination, avoiding decisions based on the results of environmental perception.

These algorithms usually involve multiple technologies such as multi-sensor fusion, state estimation, machine learning, etc.

It is even more necessary to use a large number of mathematical models and algorithms such as matrix operations, image transformation, optimization theory, and statistics to achieve intelligent decision-making.

For example, the graph isomorphism theory, although it still faces many challenges at present, there are many applications in the fields of image processing, video analysis, finding the optimal path, network flow algorithms, and efficient obstacle avoidance.

The breakthrough in mathematical tools has brought more advanced and efficient calculation methods to the algorithm judgment of AI Zhihua.

This is also the reason why the intelligent driving of Chuanhai Network Technology Company can quickly catch up with other companies that have already made in-depth plans in just two or three years.

.........

In the office, when Liu Jiaxin heard Xu Chuan ask about the research on the isomorphism of the picture and manuscript paper, she smiled and took out the sorted manuscript paper from the backpack she carried with her.

She knew that Xu Chuan's attention would definitely be focused on this, so she prepared in advance.

"I'll take a look."

Seeing the manuscript paper, Xu Chuan couldn't wait to reach out and pick it up.

Indeed, compared with breakthroughs in the field of intelligent driving, he is more concerned with research on isomorphic problems.

This involves the answer to a millennium puzzle and also involves more application areas.

Smart driving is just a part of its application.

Looking through the manuscript in his hand, Xu Chuan's eyes were filled with an interest.

“... Given two graphs G =( V G, E G ) G=(V_G, E_G)G=(V_G, E_G)

G,E G) and H =(V H, E H ) H =(V_H,E_H)H=(V H,E H).

"If there is a mapping from G to H?: V G→ V H, satisfying:?( v i )= v i′,?( v j )= v′j..."

"It's interesting. Instead of taking a broader approach to the P-class problem, we cut the isomorphic modules through quasi-polynomials and mapping functions."

"This method is a bit similar to the research method of the weak Riemann conjecture?"

Looking at the manuscript paper in his hand, Xu Chuan muttered to himself.

In fact, in simple terms, it is to give two graphs and ask whether they are exactly the same.

How to check whether the given two graphs are isomorphic and exactly the same?

One of the best ways is to simply compare each point to match all the nodes that may correspond to another graph.

But as we all know, pictures are two-dimensional planes, with 'number' points on a picture.

If, suppose a graph with N nodes, according to this matching calculation method, the number of matches is the factorial of N (1*2*3*...*N), which is far more than the order of magnitude of N.

If there are only 10 nodes in the graph, more than 3.6 million possible match checks are needed. (1*2*3......*10)

If a graph has 100 nodes, the possible number of matches will far exceed the number of atoms in the visible universe.

Therefore, this method of brute force is very impractical and is only suitable for graphs with very few nodes.

Judging from the manuscript paper in his hand, when Liu Jiaxin was studying this problem, she did not bring all the graph isomorphism problems into the P=NP type problem.

She chose to cut the isomorphic module through quasi-polynomials and mapping functions, while cutting the images, she regarded these "contrast points" as "images" in pieces.

Then simulate the four-color theorem, start with some small nodes in the first graph, and "draw" different colors for each point.

Then assume that there is a corresponding point in the second graph, and start looking for isomorphism in it, and mark these corresponding nodes with the same color after finding it.

The algorithm cycles until all possible guesses are finally verified.

This is an algorithm that is more efficient than the previous graph isomorphic problems, and the key lies in a mathematical tool in these manuscripts.

"Quadopterytic graph mapping method."

This tool is used to complete graph isomorphic efficient algorithms by connecting polynomials and mapping tools.

Although it does not solve the problem of graph isomorphism, it does not even completely summarize this problem into the category of P-type problems or NP-type problems.

But it is undeniable that this is a major breakthrough in the problem of graph isomorphism.

.........

After reading the manuscript paper in his hand, Xu Chuan breathed a sigh of relief, looked at Liu Jiaxin with a smile on his face, and said, "I didn't expect you to surprise me again. The mathematics community has been studying the problem of isomorphism for decades, and no one has ever done this level."

Liu Jiaxin shook her head gently and said, "But there is still a long way to go before solving this problem."

Xu Chuan smiled and said, "The roads are all taken little by little. Being able to find a better and simpler path means that you are on the right path."

After pausing slightly, he raised the manuscript paper in his hand and asked with a smile: "This should not be the original manuscript, can I keep it?"

This chapter is not finished yet, please click on the next page to continue reading the exciting content behind! "There are still many things worth in-depth research. I can take a good look at it when the Chinese New Year."

It is obvious that this manuscript is not the original manuscript, but a complete study after sorting, and even writing it into a paper and publishing it, there is no problem.

And it is impossible for such a wonderful paper to fully understand all the essence of it in just over a dozen minutes.

Especially when it comes to P=NP? It is conjecture that such a millennial problem, even if it is just an tentative proof of secondary problems, is of great value and worthy of in-depth exploration.

Liu Jiaxin nodded and said softly: "Of course, this is specially brought to you."

Xu Chuan smiled and said, "Then I will accept it."

"in addition....."

As he said that, he spread out the manuscript paper in his hand and continued: "I have some ideas on the tools of 'mapping isomorphism'."

Hearing this, Liu Jiaxin moved her body, sat over, and looked at the manuscript paper in her hand.

Xu Chuan stretched out his finger and pointed to a place on the manuscript paper and said, "For example, here, when you are isomorphic maps of sub-graphs, you use the single-episometric function and the bi-episometric function."

"But the function f mapped in this way usually only satisfies the mapping relationship of the homomorphic graph, and you need to further process it later."

"If we use the Weyl group mapping method of algebraic clusters, we can first simplify it to..."

In the office, Xu Chuan talked a lot about the problem of graph isomorphism and the "quasi-polynomial graphic mapping tool" he had.

In the fields of P=NP? conjecture and algorithm mathematics, his research is indeed not as good as Liu Jiaxin.

However, as a scholar at the top of the mathematics community, she is not able to compare his way of looking at problems and his feasibility in solving this problem.

Especially when Liu Jiaxin has initially improved a simplified mathematical tool for graph isomorphic problems, it is not difficult for him to find some points in this tool to optimize some points.

......

The afternoon passed almost as they discussed each other.

After chatting for the last discussion point, Xu Chuan stretched, picked up the already cold tea from the coffee table, took a sip and moistened his throat and said.

"I feel that the graph isomorphism problem may be somewhat similar to the Riemann conjecture. If you simply map and compare it to narrow its scope bit by bit, it may be difficult to solve this problem."

"Just like Riemann's conjecture, it is probably impossible to constantly compress its critical point and push it to 1/2 line. It requires a new way."

"So for the problem of graph isomorphism, my suggestion is that maybe you need to go out of the traditional way and find a new path."

"This quasi-polynomial graph mapping method is excellent, but it may not solve this problem."

After thinking seriously for a while, Liu Jiaxin nodded and said, "Well, I'll think about it carefully."

Xu Chuan smiled and said, "Don't hurry, just take it slowly. If you encounter any problems during the research process, you can come to me at any time."

"Maybe I may not be able to provide you with any help, but having more ideas for one person will definitely be better in mathematics."

Liu Jiaxin nodded and joked: "Of course, it's too pitiful to have such a good mathematician. I'm fighting alone."

Xu Chuan smiled, his eyes fell on the manuscript paper in his hand, and suddenly remembered another thing, looked at Liu Jiaxin and said, "By the way, there is another thing I want to ask you for help."

"What's wrong?"

Xu Chuan smiled and said, "If it is convenient, I need you to sort out this paper, write it into a formal paper, and then submit it to "Exploration·Mathematics."

"It will be the first journal for Explore Mathematics if you want!"

Hearing this, Liu Jiaxin nodded without hesitation and said, "No problem."

After saying that, she hesitated for a moment, thought for a while and asked again: "Is this paper enough?"

Liu Jiaxin is very clear about what the papers published in the first issue of "Exploration" and "Exploration Physics". The former is the unified theory of strong electricity, and the latter is the theory related to room temperature superconducting materials.

In contrast, her paper seems to be a bit inadequate.

Xu Chuan smiled and shook his head, saying, "If P=NP? The research on the conjecture is not qualified, what else is qualified?"

"You can be more confident, it's enough to be published in any journal in the world."
Chapter completed!