On Derandomizing Probabilistic Sublinear-Time Algorithms

There exists a positive constant alpha < 1 such that for any function
T
(
n
) les
n

^alpha
and for any problem
L
isin BPTIME(
T
(
n
)), there exists a deterministic algorithm running in poly(
T
(
n
)) time which decides L, except for at most a 2
<sup>-Omega

(T(n)

log

T(n))</sup>
fraction of inputs of length
n
.