These are quite stringent restrictions, so it was not obvious that additional memory could ever turn out. But to their surprise Buhrman and Cleve showed that if you improve the bits properly, you can really get an additional computing number from full memory.
“It was shocking for everyone,” said Loff, who was then a graduate of the Buhrman group, working on a question about memory with a friend Florian Spelman. The band soon expanded the result to an even greater class of problems and published Their total results in 2014.
They called the modern Framework Catalityc Computing, borrowing the date from chemistry. “Without a catalyst, the reaction would not continue,” he said Raghunath TerverTheoretician of complexity at the Indian Institute of Technology, Kanpur. “But the catalyst itself remains unchanged.”
Near the tree
A compact group of researchers continued to develop catalytic computers, but no one even tried to apply it to the problem of assessing the tree, which initially inspired the Kucký mission. In the case of this problem, the remaining open question was whether a compact amount of memory can be used for storage and calculations at the same time. But catalytic calculations techniques were based on additional, and the full memory was very immense. Reduce this memory and techniques no longer work.
Despite this, one youthful researcher could not wonder if there was a way to adapt these techniques to reuse memory in the tree assessment algorithm. His name was James CookAnd for him the problem with the assessment of the tree was personal: Stephen Cook, the legendary theorist of the complexity who invented him is his father. James even worked on this graduate school, although he mainly focused completely unrelated people. Before he met the original catalytic computer article in 2014, James intended to complete and leave the Software Engineering Academy. But even when he settled in his modern job, he was still thinking about catalytic computers.
“I had to understand it and see what you could do,” he said.
Over the years, James Cook tinted in a catalytic approach to the problem of assessing the tree in his free time. He talked about his progress on the 2019 symposium in honor of his father breakthrough In the theory of complexity. After the conversation, a doctoral student called him Ian Mertzwho fell in love with catalytic computers five years earlier after he learned about it as a sensitive youthful undergraduate.
“It was like a children’s print scenario,” said Mertz.
Photo: Stefan Grosser/Quanta Magazine
Cook and Mertz joined forces, and their efforts soon paid off. In 2020 they developed Algorithm This solved the problem of assessing a tree with less memory than the necessary minimum assumed by older Cook and McKenzie – although barely below this threshold. Still, it was enough to collect a $ 100 plant; Convenient for chefs, half remained in the family.
But there was still work to do. Scientists began studying trees, because it seemed that it could eventually be an example of a problem in P, which is not in L – in other words, a relatively straightforward problem that cannot be solved using very low memory. The modern Cook and Mertza method used less memory than any other tree assessment algorithm, but it still used much more than any algorithm of the problem in L. Tree assessment, but it is not turned off.
In 2023, Cook and Mertz left Improved algorithm This used much less memory – not only more than the maximum allowed problems in L. Many researchers now suspect that the assessment of the tree is finally in L, and proof is only a matter of time. Elaborate theorists may need a different approach to the problem P versus L.
Meanwhile, the results of Cook and Mertz were galvanized interest in catalytic computers, with a study of modern work Connections with randomness and the effects of enabling several mistakes By reset full memory to its original state.
“We have not finished discovering what we can do with these new techniques,” said McKenzie. “We can expect even more surprises.”
Original story reprinted with consent from How much warehouseIN Independent editor publication Simons Foundation whose mission is to escalate public understanding of science by covering the development of research and trends in mathematics and physics and life sciences.