These are very strict constraints, so it is obvious that extra memory can prove useful. But to their surprise, Buhrman and Cleve showed that if you adjust the debris the right way, you can really get extra calculations from full memory.
Love, who was a graduate student in Burman’s group at the time, worked with his classmates on memory issues, said: “It shocked everyone.” Florian Speelman. The team quickly expanded the results to a bigger problem and released Their comprehensive results 2014.
They named the new framework catalytic calculations, borrowing a term from chemistry. “The reaction would not go on without a catalyst.” Raghunath Tewaria complex theorist at the Indian Institute of Technology, Kanpur. “But the catalyst itself remains the same.”
Not far from the tree
A small group of researchers continued to further develop catalytic calculations, but no one tried to apply it to the tree evaluation problem that initially inspired the Koucký task. For this question, the remaining open question is whether it is possible to use a small amount of memory for storage and calculation at the same time. But the technique of catalytic computing depends on the extra, complete memory is very large. Contraction memory and technology no longer work.
Nevertheless, a young researcher couldn’t help asking if there is a way to adapt these techniques to repetitive memory in an algorithm on a tree. His name is James CookFor him, the question of tree evaluation is personal: Stephen Cook, the legendary complexity theorist who invented it, was his father. James even worked on it in graduate school, although he focused primarily on Totally unrelated topics. When he encountered the original catalytic computing paper in 2014, James was about to graduate and leave academia for software engineering. But even when he settled in his new job, he kept thinking about catalytic calculations.
“I have to understand it and see what can be done,” he said.
James Cook patched tree assessment issues in his spare time with a catalytic approach. He gave a conversation at the 2019 seminar to honor his father’s A pioneering work In the theory of complexity. After the speech, he was contacted by a graduate student named Ian Mertzhe fell in love with catalytic computing after he learned it was an impressive young undergraduate five years ago.
“It’s like the mark of a young bird,” said Meuse.
Photo: Stefan Grosser/Quanta Magazine
Cook and Meltz teamed up and their efforts paid off quickly. In 2020, they designed algorithm This solves the tree evaluation problem with less memory than the necessary minimum conjecture of Elder Cook and Mackenzie, although it is only below this threshold. Still, this is enough to collect $100 bets; conveniently suited to chefs, half of which stay in the family.
But there is still work to be done. Researchers have begun to look at tree evaluation, as it seems that it may eventually provide an example of a problem not in L, in other words, a relatively easy problem that cannot be solved with very little memory. Cook and Mertz’s new approach uses less memory than any other tree evaluation algorithm, but it’s still much larger than any algorithm for problems in LL Tree evaluation.
In 2023, Cook and Mertz come out Improved algorithms This use has much less memory and more than the maximum value of L. Many researchers now suspect that tree evaluation is in L after all, and it is only a matter of time before it can be proved. Complexity theorists may need different approaches to the P vs L problem.
Meanwhile, the results of Cook and Meltz sparked interest in catalytic computing and explored new works Connection with randomness And allow rare mistake Reset the full memory to its original state.
“We are not done yet to explore what these new technologies can do,” Mackenzie said. “We can expect more surprises.”
ability Reprinted with permission Quanta Magazine,,,,, Edit independent publications Simmons Foundation Its mission is to enhance public understanding of science by covering research developments and trends in mathematics and physics and life sciences.
