There is a rule in mathematics that the simpler the description, the harder the proof.
The p/np problem was first proposed by steven a. cook in 1971. In 2000, the Clay Institute of the United States announced it as one of the millennium problems, and it is still pending.
In 1971, 2000, and now, countless mathematicians have tried to challenge it.
But Lin Zhaoxi never thought that these mathematicians also included her father.
Even, she didn't realize until she fully figured out the timeline that Lao Lin was interested in the p/np problem long before it became the millennium problem.
"Boss, let's have a can of Coke." Lin Zhaoxi was very happy, she shouted with red eyes.
The waiter glanced at her and thought she was too nervous, but he still brought Coke and two plastic cups.
With a sound of "stab", Lin Zhaoxi opened the can and poured a can of Coke into two cups.
The bubbles overflowed to the mouth of the cup, and she and Lao Lin raised their glasses and touched each other lightly. subsequently. They drank more than half of the glass in one go, put down the glasses together, and wiped their mouths.
Lin Zhaoxi: "So, did the paper published by Professor Feng prove...?"
"It's not considered an official publication, it's just a draft, and it's going through the review process for official publication." Lao Lin let out a Coke-like belch.
"You really have been paying attention to this matter!"
"Cough" Lao Lin's eyes widened: "Why are you still playing tricks on Dad?"
"Because I always feel that my father is hiding something from me and deliberately not telling me."
"Imagination is too rich."
"Then why didn't you tell me that you, like Professor Zeng and Pei Zhi, have studied p/np problems?"
"Pay attention to your wording, what do you mean I am the same as them, it was me first, and..." Old Lin paused, and raised three fingers, "You knew what p/np is three months ago, and you and I are a philosophy student What are you talking about?"
Lin Zhaoxi's eyes widened, and she was choked again: "Are you a subject attack?"
Lao Lin "hummed" twice, and stopped talking proudly.
Old Lin was right.
For her, this is a long time to explore across two time and space. As far as Lao Lin is concerned, three months ago, she was a liberal arts student who had no interest in mathematics. It is difficult for him and her to have a common language in mathematics.
Fortunately, they can talk now.
Regarding p/np, after the lecture hosted and translated by Pei Zhi, Lao Lin had already told her a lot.
If a problem can find an algorithm in polynomial time, then it is a p-problem.
NP problems, on the other hand, are those for which we cannot find an answer in a fast way, but if given a solution, we can verify it in polynomial time.
Among the np problems, there is a particularly difficult class of problems called npc problems.
The npc problem has two important properties: 1. It is an NP problem; 2. All NP problems can be reduced to it.
Stephen A. cook published the plexitytheorem-proving procedures in 1971, proposing the concept of np-plete problem. And through the non-deterministic Turing machine, it is proved that the satisfiability problem (sat problem) of Boolean logic is an npc problem.
The entry point chosen by Lao Lin is the problem of exact graph isomorphism.
The business in the noodle shop was so good that the red oil noodles came out almost halfway through their chat. The hot and spicy noodle soup, served with green onion, is very appetizing.
Lao Lin picked up a thread and showed it to her: "Since the sat problem, a lot of npc problems have followed. To prove a new npc problem, you only need to reduce a known npc problem Just go to it."
"It sounds a bit simple." Lin Zhaoxi bit her chopsticks, "Then why hasn't exact graph isomorphism been proven to be an npc problem?"
"There are two possibilities." Lao Lin said, "First, the exact graph isomorphism itself is not an npc problem, so it cannot be proved."
"What about the second?"
"The second is of course that mathematicians are not capable enough to prove it. What else is there?"
"Oh..." Lin Zhaoxi took a deep breath and asked, "Then what is the specific difficulty, can you tell me in detail?"
"Where is the difficulty? First of all, it involves the depth of your understanding of graph theory." Lao Lin became interested, so he simply put down his chopsticks and began to ramble.
He said that Lin Zhaoxi listened carefully and asked if he didn't understand.
When Lao Lin talked about getting up, he lowered his head and ate two mouthfuls of noodles, chewing a few times.
The noodle shop was filled with hot air, and Lao Lin's voice was soft and cheerful. In a daze, Lin Zhaoxi looked up, and she saw Lao Lin's smile. For a moment, she couldn't even figure out which world she was in.
A bowl of noodles was almost finished, and Lin Zhaoxi was so hot that it was so hot.
From what Lao Lin said, she roughly understood what Lao Lin was trying to do and how he wanted to prove that exact graph isomorphism is an npc problem.
Even if she doesn't know Lao Lin, she is just an ordinary math student. After sitting face to face with Lao Lin, she didn't need to read the paper that Lao Lin was accused of plagiarizing to be sure that Lao Lin was an expert in this field, and he didn't need to plagiarize other people's academic achievements.
Lao Lin was still very happy, and the creases at the corners of his eyes were deeper because he had been squinting just now.
"I probably understand." She put down her chopsticks and took a sip of the spicy soup: "So Professor Feng's proof is right or not, do you know?"
"Aren't you going to school for the graduation ceremony?" Lao Lin lit up his phone and checked the time, "It's still time to call Didi."
Lin Zhaoxi frowned slightly, and Lao Lin interrupted her question about Professor Feng's detailed proof for the rare second time.
"Graduation is not as important as you," she said.
"Too gross."
"Why don't you ask me, who did you meet at Yongchuan University?"
"who?"
"I haven't met anyone."
Lao Lin: "..."
The noodle shop was steaming hot, even though there was an air conditioner, Lin Zhaoxi was still sweating a little.
"I have one last question." The Coke in the cup had already been emptied, Lin Zhaoxi twirled the cup half a circle and raised her head.
She asked: "Is Professor Feng Deming's paper on graph isomorphism related to the article you were accused of plagiarizing?"
—
Lin Zhaoxi thought, her father has always been a straightforward person.
It’s so frank that it doesn’t matter. Tell her since you were young that you don’t have a mother, and you’re so frank that you can tell her where to find the notice that he was fired.
Now, Lao Lin not only avoided the question about Professor Feng's proof twice. And after she finished questioning, he stood up for the first time, went to the waiter to check out and pay, and then walked out of the store.
The plastic curtain was opened and closed, and Lao Lin was wearing a formal suit and shirt, with obvious sweat stains on his back.
She looked back and saw the cardboard box he had forgotten to take away at her feet.
—
The weather is hot in midsummer, and all the brilliant sunlight is filtered through the leaves of the sycamore tree, leaving only patches of light on the ground.
It's not uncommon for Alzheimer's patients to forget a cardboard box they brought.
Lin Zhaoxi picked up the cardboard box, amazed at its heavy weight. There was the logo of Lao Lin's accounting firm on the box, which seemed to be the company's material.
The noodle shop is within walking distance from Lao Lin's company. When she walked out, Lao Lin had disappeared.
She didn't think much about anything else, and walked to Lao Lin's company with the cardboard box in her arms, thinking that Lao Lin had probably gone back to work, so she wanted to send the things back.
Lao Lin rarely seems to be so secretive.
Even when she asked questions such as "Did I affect your life", Lao Lin would use "national laws and regulations" to laugh.
He had never refused to answer with silence like now.
It was almost two o'clock, and the entrance of Lao Lin's company was quiet.
The front desk lady yawned through the sliding door, and Lin Zhaoxi smiled at her holding the cardboard box.
The sliding door was opened, and the cold air rushed in, and Lin Zhaoxi shivered.
"Hello." The receptionist immediately got up, bowed politely, and smiled, "Who are you looking for?"
"Ah, I'm here to look for..." Lin Zhaoxi paused, then changed her words, "Lin Zhaosheng."
"Ah, accountant Lin, he left today."
Lin Zhaoxi hugged the cardboard box and stood there dumbfounded.
When going out in the morning, Lao Lin rarely saw a suit and leather shoes. She was still teasing Lao Lin about whether she was going to meet the girl she liked, but now that she thought about it, she was too stupid.
Probably because he left his job today, Lao Lin specially dressed very formally. People of the older generation like him always have this habit.
Front desk lady: "Are you accountant Lin?"
"I am her daughter." Lin Zhaoxi recovered.
"Sorry, sorry, I think you are a little strange, I didn't recognize you before."
Because this is my second time here.
The lady at the front desk quickly poured a glass of water, came out, and greeted her, "Would you like to sit down for a while and call Accountant Lin?"
Lin Zhaoxi was sweating profusely, put down the cardboard box, took out her phone a little embarrassedly, and explained: "I was eating with him just now, and he left a cardboard box in the store, and I want to send it back to him."
There were indeed a few missed calls on the phone, but they were not from Lao Lin, but the series of fatal calls from their monitor. The class monitor sent her a few messages like 'Lin Zhaoxi, why didn't you come to the graduation ceremony', 'What happened'... and so on.
She hurriedly replied—suddenly something happened at home, sorry, sorry, please help me get it.
The monitor didn't reply immediately, the time was two o'clock in the afternoon, and the graduation ceremony should officially begin.
Lin Zhaoxi put down her phone and heard the lady at the front desk say, "The box is full of scratch paper that accountant Lin took away, it should be something your father wants to bring back. We divided everything else, not even the prickly pear he raised. "
Lin Zhaoxi saw that there was indeed a small prickly pear on the front desk, which looked a bit malnourished, but the flowerpot was very cute.
Did you take nothing with you when you resigned, only this cardboard box? Lin Zhaoxi looked at the seal of the box that was closed at will, and wanted to open it for a moment.
"Isn't everything written on the accountant's draft paper a company secret, you should withhold it when he resigns!" She laughed, "Moving makes me almost paralyzed."
"That's right, there are a lot of them in the office upstairs. Our manager also joked that he wasted so much draft paper in the company and would deduct money from accountant Lin!"
Just as Lin Zhaoxi was about to answer, the phone flickered again.
Pei Zhi—what happened
Lin Zhaoxi subconsciously picked up the phone, but when she touched the screen, she found it difficult to reply, and in the end, she had no choice but to put the phone down.
At this moment, the sliding door of the hall was opened again, and the heat wave rolled in.
A middle-aged man in a suit and leather shoes walked into the lobby, and the receptionist quickly stood up: "Manager Zhang, are you back?"
Lin Zhaoxi also got up subconsciously.
"This is Accountant Lin's daughter." The front desk lady introduced.
"Yo, Lao Lin's daughter is so beautiful!" Manager Zhang looked very kind, and he also saw the cardboard box she put on the coffee table, and reacted quickly, "Old Lin forgot to take it, and you brought it back for her?"
Lin Zhaoxi nodded helplessly.
"Hey." Manager Zhang walked a few steps towards the elevator entrance, and suddenly turned to her and said, "Do you want to visit your father's office before it's cleaned?"