In this paper, we show that efficient algorithms for some problems tha
t require limited nondeterminism imply the subexponential simulation o
f nondeterministic computation by deterministic computation. In partic
ular, if cliques of size O(log n) can be found in polynomial time, the
n nondeterministic time f(n) is contained in deterministic time 2(O)(r
oot f(n)polylog f(n)).