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:
“I swear to keep the dead upon my mind,/Disdain for all time to be overglad./Among spring flowers, under summer trees./By chilling autumn waters, in the frosts/Of supercilious winter—all my days/I’ll have as mentors those reproving ghosts.”
—Gwendolyn Brooks (b. 1917)
“Though seas and land be ‘twixt us both,
Our faith and troth,
Like separated souls,
All time and space controls:
Above the highest sphere we meet
Unseen, unknown, and greet as angels greet.”
—Richard Lovelace (1618–1658)
“By the rivers of Babylon, there we sat down, yea, we wept, then we remembered Zion.”
—Bible: Hebrew Psalm CXXXVII (l. CXXXVII, 1)