  A classic result of Paul, Pippenger, Szemer\'edi and Trotter states that
DTIME(n) is strictly contained in NTIME(n). The natural question then arises:
could DTIME(t(n)) be contained in NTIME(n) for some superlinear
time-constructible function t(n)? If such a function t(n) does exist, then
there also exist effective nondeterministic guessing strategies to speed up
deterministic computations. In this work, we prove limitations on the
effectiveness of nondeterministic guessing to speed up deterministic
computations by showing that the existence of effective nondeterministic
guessing strategies would have unlikely consequences. In particular, we show
that if a subpolynomial amount of nondeterministic guessing could be used to
speed up deterministic computation by a polynomial factor, then P is strictly
contained in NTIME(n). Furthermore, even achieving a logarithmic speedup at the
cost of making every step nondeterministic would show that SAT is in NTIME(n)
under appropriate encodings. Of possibly independent interest, under such
encodings we also show that SAT can be decided in O(n lg n) steps on a
nondeterministic multitape Turing machine, improving on the well-known O(n(lg
n)^c) bound for some constant but undetermined exponent c which is at least 1.
