Why can you add a fully stable tablet engine more powerful

These are very strict restrictions, so it was not clear that the additional memory could be useful at all. But for their amazement, Buhrman and Cleve showed that if you adjust bits in the right way, you can really get an additional mathematical attraction from full memory.

“This was a shock to everyone,” said Loew, who was a graduate student in Bouhraman’s group at the time. Florian Spieman. The team soon extended the result to a larger category of problems Their results combined In 2014.

They named the new incentive computing of the frame and borrowing the term of chemistry. He said: “Without the catalyst, the reaction did not go.” Raghunath TewariTheorist of the complexity at the Indian Institute of Technology, Kanbur. “But the catalyst is still unchanged.”

Not far from the tree

A small group of researchers continued to develop incentive computing, but no one even tried to apply it to the problem of evaluating trees that initially inspired Koucký. For this problem, the remaining open question was whether a small amount of memory could be used for storage and account simultaneously. But incentive computing techniques depended on the complete additional memory very large. Reducing that memory and techniques no longer works.

However, a young researcher has not been able to help ask whether there was a way to adapt these techniques to reuse the memory in the tree evaluation algorithm. His name was James CookAnd for him, the problem of evaluating trees was personal: Stephen Cook, the legendary sophistication view he invented, is his father. James had worked on him at the Graduate School, although he mostly focused Topics completely relevant. By the time when he faced the original incentive computing paper in 2014, James was about to graduate and leave the academic circles of software engineering. But even when he settled in his new job, he was thinking about incentive computing.

He said: “I had to understand that and see what could be done.”

For years, James Cook was exposed to a catalyst approach to the problem of evaluating trees in his spare time. He recently delivered his progress at the 2019 symposium in honor of his father Pioneer work In the theory of complexity. After talking, he was contacted by a graduate student called Ian MertzWho fell in love with incentive computing five years ago after identifying it as a young student.

“It was like the scenario of the bird’s printing,” said Mertz.

Cook and Mertz joined the efforts, and soon paid their efforts. In 2020, they were invented Algorithm This is the solution to the problem of evaluating trees with a lesser memory than the minimum needed by Elder Cook and McKenzie – although it was barely less than that threshold. However, this was sufficient to raise the bet of $ 100; Comfortable for chefs, half of which remain in the family.

But there is still a job to do. Researchers began to study the evaluation of trees because it seemed as if it might finally provide an example of a problem with P not in L – in other words, a relatively easy problem that cannot be solved using a very few memory. The new Cook and MERTZ method used a lesser memory than any algorithm to assess other trees, but it is still used much more than any algorithm for a problem in evaluating L., but not outside it.

In 2023, Cook and Mertz came out with Improving algorithm It has used a much lower memory – there is nothing more than the maximum allowed for problems in L. Many researchers now suspect that the evaluation of trees in L after all, and that the evidence is just a matter of time. The theorists may need a different approach to the problem of P against L.

Meanwhile, the results of Cook and Mertz have stimulated interest in incentive computing, while exploring new works Random communications And the effects of allowing A few mistakes In reset the full memory of its original condition.

“We have not finished exploring what we can do with these new technologies,” said McKenzi. “We can expect more surprises.”

---

The original story Recal it with permission from Quanta magazineand An independent editorial publication for Simonz Foundation Its mission is to enhance the general understanding of science by covering research developments and trends in mathematics, physical sciences and life.