These are fairly strict constraints, it was therefore not easy that additional memory could be useful. But to their surprise, Buhrman and Cleve have shown that if you change the pieces in the right way, you can really get an additional calculation punch from a full memory.
“It was a shock for everyone,” said Loff, who was a student graduated from the Buhrman group at the time, working on the issue of memory with his student colleague Florian Speelman. The team quickly extended the result to an even greater class of problems and published their combined results in 2014.
They appointed the new framework for catalytic IT, borrowing a term from chemistry. “Without the catalyst, the reaction would not have proceeded,” said Raghunath TewariTheorist of complexity at the Indian Institute of Technology, Kanpur. “But the catalyst itself remains unchanged.”
Not far from the tree
A small band of researchers continued to develop catalytic computers more, but no one even tried to apply it to the problem of assessing trees which had initially inspired the quest for Koucký. For this problem, the remaining open question was whether a small amount of memory could be used simultaneously for storage and calculation. But the techniques of catalytic IT were based on additional memory, the full memory being very large. Reduce this memory and the techniques no longer work.
However, a young researcher could not help wondering if there was a way to adapt these techniques to reuse memory in an algorithm for the assessment of trees. His name was James CookAnd for him, the problem of assessing trees was personal: Stephen Cook, the theorist of the legendary complexity which invented him, is his father. James had even worked on higher education on it, although he focuses above all on Completely unrelated subjects. As he met the original catalytic computer document in 2014, James was on a graduate and leaving the university world for software engineering. But even he had settled in his new job, he continued to think of catalytic computers.
“I had to understand it and see what could be done,” he said.
For years, James Cook has tied a catalytic approach to the problem of assessing trees during his free time. He gave a conference on his progress during a 2019 symposium in honor of his father revolutionary work In the theory of complexity. After the conference, he was approached by a graduate student appointed Ian MertzWho had fallen in love with catalytic computers five years earlier after learning it as a young impressionable student.
“It was like a baby bird printing scenario,” said Mertz.
Photography: Stefan Grosser / Quanta Magazine
Cook and Mertz have united their strengths and efforts quickly paid off. In 2020, they designed an algorithm This resolved the problem of assessing trees with less memory than a minimum necessary conjectured by the elder Cook and McKenzie – although it was barely below this threshold. However, it was enough to collect the bet of $ 100; Almost for cooks, half stayed in the family.
But there was still work to do. The researchers had started to study the assessment of trees because it seemed that he could finally provide an example of a P problem which is not in L – in other words, a relatively easy problem which cannot be resolved using very little memory. The new method of Cook and Mertz used less memory than any other trees evaluation algorithm, but it has always used much more than any algorithm for a problem in the assessment of L. was down, but not.
In 2023, Cook and Mertz went out with a improved algorithm This used much less memory – very more than the maximum authorized for problems at L. Many researchers now suspect that the assessment of trees is in the after all, and that proof is only a matter of time. The theorists of complexity may need a different approach to the problem P against L.
Meanwhile, the results of Cook and Mertz have galvanized interest in catalytic computers, with new works exploring RECOMMENT CONNECTIONS and the effects of allowing a little errors By reset the full memory to its original state.
“We have not finished exploring what we can do with these new techniques,” said McKenzie. “We can expect even more surprises.”
Original story reprinted with the permission of Quanta Magazine,, an independent editorial publication of Simons Foundation whose mission is to improve the understanding of the public of science by covering the developments of research and the trends of mathematics and physical sciences and life.
