Why Adding a Full Hard Drive Can Make a Computer 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 student of high school studies at the Bouhraman Group at that time. The team soon extended the result to a larger category of problems, and published their joint results in 2014.
They named the new incentive computing of the frame and borrowing the term of chemistry. “Without the catalyst, the reaction did not continue,” said Ragonath Toyari, one of the theorists of the complexity at the Indian Institute of Technology. “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 Cook, and for him, the problem of evaluating trees was personal: Stephen Cook, the legendary complexor theorists that he invented, is his father. James was working on this at the Graduate School, although he often focused on completely unrelated topics. 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 talked about his progress at the 2019 symposium in honor of his pioneering father’s work in the theory of complexity. After the conversation, a high school student named Ian Mertz, who fell in love with incentive computing, called him five years ago after learning about it as a young student.
“It was like the scenario of the bird’s printing,” said Mertz.
Photo: Stephen Groser Magazine/Quanta
Cook and Mertz joined the efforts, and soon paid their efforts. In 2020, they invented an algorithm that solved the problem of evaluating trees with less memory than the minimum for guessing 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 an improved algorithm that used a much lower memory – it is 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 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 the fossil computing, with new works that explore communications to randomness and the effects of allowing some errors in reseting the full memory to its original state.
“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 magazine, 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.
2025-03-30 11:00:00
