Disperser
A disperser is a one-sided extractor. Where an extractor requires that every event gets the same probability under the uniform distribution and the extracted distribution, only the latter is required for a disperser. So for a disperser, an event
A
⊆
{
0
,
1
}
m
{\displaystyle A\subseteq \{0,1\}^{m}}
we have:
P
r
U
m
[
A
]
>
1
−
ϵ
{\displaystyle Pr_{U_{m}}[A]>1-\epsilon }
Definition (Disperser): A
(
k
,
ϵ
)
{\displaystyle (k,\epsilon )}
-disperser is a function
D
i
s
:
{
0
,
1
}
n
×
{
0
,
1
}
d
→
{
0
,
1
}
m
{\displaystyle Dis:\{0,1\}^{n}\times \{0,1\}^{d}\rightarrow \{0,1\}^{m}}
such that for every distribution
X
{\displaystyle X}
on
{
0
,
1
}
n
{\displaystyle \{0,1\}^{n}}
with
H
∞
(
X
)
≥
k
{\displaystyle H_{\infty }(X)\geq k}
the support of the distribution
D
i
s
(
X
,
U
d
)
{\displaystyle Dis(X,U_{d})}
is of size at least
(
1
−
ϵ
)
2
m
{\displaystyle (1-\epsilon )2^{m}}
.
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