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("n") steps and at most o("n") cells of its read-write tapes.