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New proof dramatically compresses space needed for computation
Surprising new work bucks 50 years of assumptions about the trade-offs between computation space and time
Once upon a time computers filled entire rooms, reading numbers from spinning tapes and churning them through wires to do chains of basic arithmetic. This idea is at the core of Williams’s result: any problem can be transformed into one you can solve by cleverly reusing space, deftly cramming the necessary information into just a square-root number of bits. “Before this result, there were problems you could solve in a certain amount of time, but many thought you couldn’t do so with such little space.” Williams’s finding, he adds, is “a step in the right direction that we didn’t know how to take.”
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