For nearly 50 years theorists believed that if solving a problem takes t steps, it should also need roughly t bits of memory: 100 steps - 100bits. To be exact t/log(t).
Ryan Williams found that any problem solvable in time t needs only about sqrt(t) bits of memory: a 100-step computation could be compressed and solved with something on the order of 10 bits.
For nearly 50 years theorists believed that if solving a problem takes t steps, it should also need roughly t bits of memory: 100 steps - 100bits. To be exact t/log(t).
Ryan Williams found that any problem solvable in time t needs only about sqrt(t) bits of memory: a 100-step computation could be compressed and solved with something on the order of 10 bits.