Stephen A. Bloch, Jonathan F. Buss, Judy Goldsmith

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 >>>

Emanuele Viola

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 >>>