We define the sharply bounded hierarchy, SBHQL, a hierarchy of
classes within P, using quasilinear-time computation and
quantification over values of length log n. It generalizes the
limited nondeterminism hierarchy introduced by Buss and Goldsmith,
while retaining the invariance properties. The new hierarchy has
several alternative characterizations.

We define ... more >>>

We prove several new results regarding the relationship between probabilistic time, BPTime(t), and alternating time, \Sigma_{O(1)} Time(t). Our main results are the following:

1) We prove that BPTime(t) \subseteq \Sigma_3 Time(t polylog(t)). Previous results show that BPTime(t) \subseteq \Sigma_2 Time(t^2 log t) (Sipser and Gacs, STOC '83; Lautemann, IPL '83) ... more >>>