Computational complexity theory

"Phrased in qualitative terms, Williams’ second result may sound like the long-sought solution to the P versus PSPACE problem. 

"The difference is a matter of scale. P and PSPACE are very broad complexity classes, while Williams’ results work at a finer level. 


"That’s a daunting challenge, akin to prying apart a sidewalk crack with a crowbar until it’s as wide as the Grand Canyon. But it might be possible to get there by using a modified version of Williams’ simulation procedure that repeats the key step many times, saving a bit of space each time. 

"It’s like a way to repeatedly ratchet up the length of your crowbar —make it big enough, and you can pry open anything. That repeated improvement doesn’t work with the current version of the algorithm, but researchers don’t know whether that’s a fundamental limitation."

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