These are rather strict constraints, so it was not clear that extra memory would prove useful. But to my surprise, Buhrman and Cleve showed that if you tweak the bits in the right way, you can get extra computational vitality from full memory.
“It was shocking for everyone,” said Loff, who was a graduate student in Buhrman’s group at the time. Florian Spellman. The team quickly extended the results into a larger class of issues and published them The total results 2014.
They called the new framework catalytic computing and borrowed the terminology from chemistry. “Without the catalyst, the reaction would not have progressed.” Raghunath TewariKanpur, a complex theorist at Indian Institute of Technology. “But the catalyst itself remains the same.”
Not too far from the tree
A small number of researchers continued to develop more catalytic computing, but none of them tried to apply it to the problem of tree assessment that first influenced Koucký’s quest. Regarding that question, the remaining open question was whether a small amount of memory can be used simultaneously for storage and calculations. However, catalytic computing technology relied on the fact that extra full memory was very large. If you reduce that memory, the technique will no longer work.
Still, one young researcher could not question whether there was a way to adapt these techniques to reuse memory with tree evaluation algorithms. That’s what his name was James Cookand for him, the question of tree evaluation was personal. Stephen Cook, the legendary complexity theorist who invented it, is his father. James was even working in graduate school, but he was mostly focused. A completely unrelated subject. By the time he came across the original catalytic computing paper in 2014, James had graduated and was about to leave Academia for software engineering. But even as he settled on a new job, he continued to think about catalytic computing.
“I had to understand that and see what I could do,” he said.
For years, James Cook messed around with his catalytic approach to the tree assessment problem in his spare time. He spoke about his progress at the 2019 symposium in honor of his father. A groundbreaking job Complexity theory. After the lecture, he was approached by a graduate student named Ian Martzafter learning about it as an impressive young undergraduate, I fell in love with catalytic computing five years ago.
“It was like a baby bird imprinting scenario,” Martz said.
Photo: Stefan Grosser/Quanta Magazine
Cook and Meltz joined forces and their efforts were quickly rewarded. In 2020, they came up with it algorithm It solved the tree assessment problem with less memory than the minimum required by ElderCook and Mackenzie, but it was barely below that threshold. Still, it was enough to collect in a $100 bet. It was convenient for chefs, and half of them remained in the family.
But there was still work to do. The researchers had begun researching tree assessments as it seemed possible that they could ultimately provide an example of a P problem that is not L. Cook and Mertz’s new method used less memory than any other tree evaluation algorithm, but L. The tree rating was not down, but it was not.
In 2023, Cook and Meltz appeared. Improved algorithms This was using much less memory for LES. This does not exceed the maximum for L problems. Many researchers suspect that after all, the tree’s assessment is in L, and that the evidence is only a matter of time. Complex theorists may require a different approach to the P-V-L problem.
Meanwhile, Cook and Mertz’s results raise interest in catalytic computing and new works are exploring Connecting to randomness And the effect of allowing a a bit error When resetting full memory to its original state.
“We haven’t finished exploring what these new techniques can do,” Mackenzie said. “We can expect even more surprises.”
Original Story Reprinted with permission from Quanta Magazine, Edited independent publications of Simons Foundation Its mission is to enhance public understanding of science by covering research and development and trends in mathematics and physical sciences and life sciences.
