There is a rule in mathematics that the simpler the description, the more difficult the proof.

The P/NP problem was first proposed by Steven A. Cook in 1971. In 2000, the Clay Institute in the United States announced it as one of the Millennium Problems, and it still remains on the list.

In 1971, 2000, and till now, countless mathematicians have come forward one after another to challenge it.

Lin Chaoxi had never thought before that these mathematicians also included her father.

In fact, it was not until she had completely sorted out the timeline that she realized that Lao Lin had been interested in the p/np problem long before it became the Millennium Problem.

"Boss, give me a can of Coke." Lin Chaoxi was very happy. She shouted loudly with red eyes.

The waiter glanced at her and thought she was too crazy, but still brought her a Coke and two plastic cups.

With a "sizzle" sound, Lin Chaoxi opened the can and poured two cups of Coke.

The foam gurgled and overflowed to the rim of the cup. She and Lao Lin raised their glasses and clinked them together. Then, they drank most of the cup in one breath, put down the cup and wiped their mouths.

Lin Chaoxi: "So, did Professor Feng's paper prove...?"

“It’s not a formal publication. It’s just a draft. It’s going through the review process for a formal publication.” Lao Lin burped with a cola-flavored burp.

"You have been paying attention to this matter!"

"Ahem." Old Lin's eyes widened: "Why are you setting a trap for Dad?"

"Because I always feel that my father is hiding something from me and deliberately not telling me."

"You have too much imagination."

"Then why didn't you tell me that you, like Professor Zeng and Pei Zhi, also studied the p/np problem?"

"Watch your wording. What do you mean I'm the same as them? It was obviously me first, and..." Old Lin paused and raised three fingers. "Three months ago you knew what p/np was. What am I talking about with a philosophy student like you?"

Lin Zhaoxi's eyes widened, and he was choked again: "Does this count as an academic attack?"

Lao Lin snorted twice and said nothing proudly.

Lao Lin is right.

For her, this was a long period of exploration across two time and space. For Lao Lin, three months ago, she was still a liberal arts student with no interest in mathematics. It was difficult for him and her to have a common language in mathematics.

But thankfully, they can talk now.

Regarding p/np, Lao Lin had actually told her a lot after the lecture hosted and translated by Pei Zhi.

If a problem can be solved in polynomial time, then it is a p-problem.

NP problems are those that we cannot find answers to using fast methods, but if a solution is given, we can verify it in polynomial time.

Among NP problems, there is a particularly difficult type of problem, called NPC problems.

The NPC problem has two important characteristics: 1. It is an NP problem; 2. All NP problems can be reduced to it.

Stephen A. Cook published the plexity theory-proving procedures in 1971, proposing the concept of NP-plete problem. He also proved that the satisfiability problem of Boolean logic (SAT problem) is an NPC problem through non-deterministic Turing machines.

The entry point chosen by Lao Lin is the problem of precise graph isomorphism.

The noodle shop was very busy, and the spicy noodles were served when they were halfway through their conversation. The hot noodle soup, paired with the green onions, was very appetizing.

Lao Lin raised an aspect and showed her: "Since the SAT problem came up, a lot of NPC problems followed. To prove a new NPC problem, you just need to reduce a known NPC problem to it."

"It sounds a bit simple." Lin Zhaoxi bit his chopsticks, "Then why hasn't it been proven that exact graph isomorphism is an NPC problem?"

"There are two possibilities," said Lao Lin. "First, exact graph isomorphism itself does not belong to the NPC problem, so it cannot be proved."

"And the second one?"

"The second reason is, of course, that mathematicians are not capable enough to prove it. What else is there?"

"Oh..." Lin Chaoxi took a sip of noodles and asked, "What are the specific difficulties? Can you tell me in detail?"

"Where's the difficulty? First of all, it involves the depth of your understanding of graph theory." Lao Lin became interested and simply put down his chopsticks and started chattering.

He said, Lin Chaoxi listened carefully and asked questions when he didn't understand.

Lao Lin became excited as he spoke. He lowered his head and took two mouthfuls of noodles, chewing them a few times with big mouthfuls.

The noodle shop was filled with steam, and Lao Lin's voice was gentle and cheerful. In a trance, Lin Chaoxi looked up and saw Lao Lin's smile. For a moment, she even couldn't figure out which world she was in.

After almost finishing the bowl of noodles, Lin Chaoxi was thoroughly enjoying the spiciness.

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 was an NPC problem.

Even if she didn't know Lao Lin, as just an ordinary math student, after sitting and eating noodles with Lao Lin, she didn't even 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 had no need to plagiarize other people's academic achievements.

Lao Lin was still very happy, and the wrinkles at the corners of his eyes appeared even deeper because he had been squinting just now.

"I roughly understand it." She put down her chopsticks and drank a mouthful of spicy soup: "So do you know whether Professor Feng's proof is correct or not?"

"Aren't you going to the school to attend the graduation ceremony?" Lao Lin turned on his phone and checked the time. "You can still catch up by calling Didi now."

Lin Chaoxi frowned slightly, and Old Lin interrupted her for the second time, rarely, to ask about Professor Feng's detailed proof.

"The graduation ceremony is not as important as you," she said.

“That’s too corny.”

"Why don't you ask me who I met at Yongchuan University?"

"who?"

“I haven’t met anyone.”

Lao Lin: “…”

The noodle shop was filled with steam, and even though there was air conditioning, Lin Chaoxi still broke out in a thin layer of sweat.

"I have one last question." The Coke in the cup had already been drunk. Lin Chaoxi held the rim of the cup, turned it half a circle, and looked up.

She asked: "Is there any connection between Professor Feng Deming's paper on graph isomorphism and the paper you were accused of plagiarizing?"

——

Lin Chaoxi thought that her father had always been an open and honest person.

Be frank enough to tell her from a young age that you have no mother, and be frank enough to tell her where she can find the notice that he was fired.

Now, not only did Lao Lin evade the question about Professor Feng's proof twice, but after she asked him again, he stood up for the first time and went to the waiter to pay the bill, and then walked out of the store.

The plastic curtain opened and closed. Lao Lin was wearing a formal suit with obvious sweat stains on his back.

She looked back and saw the cardboard box at her feet that he had forgotten to take away.

——

It was hot in midsummer, and all the brilliant sunlight was filtered through the leaves of the sycamore trees, leaving only patches of light on the ground.

It's normal for an Alzheimer's patient to forget a cardboard box they brought.

Lin Chaoxi picked up the cardboard box and was surprised at its heaviness. The box had the logo of the accounting firm where Lin worked, and it looked like it contained company materials.

The noodle shop was within walking distance of Lao Lin's company. When she walked out the door, Lao Lin was gone.

She didn't think much about it and walked towards Lao Lin's company with the cardboard box in her arms. She thought that Lao Lin had probably gone back to work, so she wanted to send the things back.

It seems that Lao Lin rarely expresses such deep regrets.

Even when she asked him questions like "Have I affected your life?", Lao Lin would always laugh it off by saying "national laws and regulations".

He had never refused to answer with silence like he did now.

It was almost two o'clock and the entrance of Lao Lin's company was quiet.

The receptionist yawned in the sliding door, and Lin Chaoxi smiled at her while holding the cardboard box.

The sliding door opened, and the cold air blew in his face, making Lin Chaoxi shudder.

"Hello." The receptionist immediately stood up, bowed politely, and smiled. "May I ask who you are looking for?"

"Ah, I'm here to see..." Lin Chaoxi paused and changed his words, "Lin Zhaosheng."

"Ah, Accountant Lin? He resigned today."

Lin Chaoxi stood there holding the cardboard box.

When he went out in the morning, Lao Lin was wearing a suit and tie, which was rare. She was still teasing Lao Lin whether he was going to meet the girl he liked. Now she thought that she was too stupid.

Maybe because he was leaving his job today, Lao Lin dressed very formally. Old people like him always have this habit.

Front desk lady: "Are you from Accountant Lin?"

"I'm her daughter." Lin Chaoxi came back to his senses.

"Sorry, sorry, you look a little strange to me. I didn't recognize you before."

Because this is my second time here.

The receptionist 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 Chaoxi was sweating profusely. He put down the carton, took out his phone a little embarrassedly, and explained: "I was just eating with him, and he left a carton in the store, and I wanted to return it to him."

There were indeed a few missed calls on her phone, but they were not from Lao Lin, but from their class monitor, who kept calling her. The monitor also sent her several messages like "Lin Chaoxi, why didn't you come to the graduation ceremony?" and "What happened?"

She quickly replied, “Something happened suddenly at home. Sorry, sorry. Could you please take care of it for me?”

The monitor did not reply immediately. It was two o'clock in the afternoon and the graduation ceremony should have officially begun.

Lin Chaoxi put down his phone and heard the receptionist say, "The box is full of draft papers that Accountant Lin took away. They must be the things your father wanted to take back. He gave us everything else. He didn't even take the cactus he raised."

Lin Chaoxi saw that there was indeed a small cactus on the front desk. It looked a little malnourished, but the flowerpot was very cute.

Did you take nothing with you when you left your job, except this cardboard box? Lin Chaoxi looked at the box that was casually sealed, and for a moment he wanted to open it and take a look.

"Aren't all the things written on the accounting draft paper company secrets? You should have kept them after he resigned!" She laughed, "I was almost paralyzed from moving them."

"Yes, there are still a lot of them in the office upstairs. Our manager even joked that he would deduct Lin's money for wasting so much draft paper!"

Lin Chaoxi was about to answer when his phone flashed again.

Pei Zhi - what happened?

Lin Zhaoxi subconsciously picked up the phone, but when she touched the screen, she found it difficult to reply. In the end, she had to put the phone down.

At this moment, the sliding door of the hall opened again, and a wave of heat rolled in.

A middle-aged man in a suit and tie walked into the lobby, and the receptionist stood up quickly: "Manager Zhang, you're back?"

Lin Chaoxi also stood up subconsciously.

"This is Accountant Lin's daughter," the receptionist introduced.

"Oh, Miss Lin is so pretty!" Manager Zhang looked very kind. He also saw the cardboard box she put on the coffee table and reacted quickly, "Mr. Lin forgot to take it, so you carried it back for her?"

Lin Zhaoxi nodded helplessly.

"Hey." Manager Zhang walked a few steps toward the elevator and suddenly turned back to her and said, "Would you like to visit your father's office before the cleaner cleans it?"