Part 6/10:
Continuing into the realm of multitape Turing machines—which utilize multiple tapes and hence allow for a greater efficiency in reading and writing—Williams's recent revelations resonate as a continuation of this historic narrative. Prior theories held that reducing the space-time graph for multitape machines would be exceedingly difficult, if not impossible, but Williams's findings indicate otherwise.
By leveraging each machine's multiple tapes, computations can now be carried out more expeditiously than previously conceived. Williams posited that any computation originally restricted in time, yet unbound in space, could be executed using substantially less—precisely SQRT(T log T)—illustrating an unprecedented level of efficiency in the use of space.