Time/space SAT Tradeoff
Currently we have no way to prove that Boolean satisfiability problem (often abbreviated as SAT), which is NP-complete, requires exponential (or at least super-polynomial) time (this is the famous P versus NP problem), or linear (or at least super-logarithmic) space to solve. However, in the context of space-time tradeoff, one can prove that SAT cannot be computed if we apply constraints to both time and space. L. Fortnow, Lipton, D. van Melkebeek, and A. Viglas proved that SAT cannot be computed by a Turing machine that takes at most O steps and at most O cells of its read-write tapes.
Read more about this topic: Richard J. Lipton
Famous quotes containing the words time, space and/or sat:
“A set of ideas, a point of view, a frame of reference is in space only an intersection, the state of affairs at some given moment in the consciousness of one man or many men, but in time it has evolving form, virtually organic extension. In time ideas can be thought of as sprouting, growing, maturing, bringing forth seed and dying like plants.”
—John Dos Passos (1896–1970)
“If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take us as long to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking. All recollected times undergo, accordingly, what M. Ribot calls foreshortening; and this foreshortening is due to the omission of an enormous number of facts which filled them.”
—William James (1842–1910)
“What brought them there so far from their home,
Cuchulain that fought night long with the foam,
What says the Clock in the Great Clock Tower?
Niamh that rode on it; lad and lass
That sat so still and played at the chess?
What but heroic wantonness?”
—William Butler Yeats (1865–1939)