<s>
A	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
is	O
a	O
generalized	O
data	B-General_Concept
structure	I-General_Concept
of	O
Bloom	B-Algorithm
filter	I-Algorithm
,	O
that	O
is	O
used	O
to	O
test	O
whether	O
a	O
count	O
number	O
of	O
a	O
given	O
element	O
is	O
smaller	O
than	O
a	O
given	O
threshold	O
when	O
a	O
sequence	O
of	O
elements	O
is	O
given	O
.	O
</s>
<s>
As	O
a	O
generalized	O
form	O
of	O
Bloom	B-Algorithm
filter	I-Algorithm
,	O
false	O
positive	O
matches	O
are	O
possible	O
,	O
but	O
false	O
negatives	O
are	O
not	O
–	O
in	O
other	O
words	O
,	O
a	O
query	O
returns	O
either	O
"	O
possibly	O
bigger	O
or	O
equal	O
than	O
the	O
threshold	O
"	O
or	O
"	O
definitely	O
smaller	O
than	O
the	O
threshold	O
"	O
.	O
</s>
<s>
Most	O
of	O
the	O
parameters	O
are	O
defined	O
same	O
with	O
Bloom	B-Algorithm
filter	I-Algorithm
,	O
such	O
as	O
m	O
,	O
k	O
.	O
m	O
is	O
the	O
number	O
of	O
counters	O
in	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
,	O
which	O
is	O
expansion	O
of	O
m	O
bits	O
in	O
Bloom	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
An	O
empty	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
is	O
a	O
m	O
counters	O
,	O
all	O
set	O
to	O
0	O
.	O
</s>
<s>
Similar	O
to	O
Bloom	B-Algorithm
filter	I-Algorithm
,	O
there	O
must	O
also	O
be	O
k	O
different	O
hash	B-Error_Name
functions	I-Error_Name
defined	O
,	O
each	O
of	O
which	O
maps	B-Algorithm
or	O
hashes	B-Error_Name
some	O
set	O
element	O
to	O
one	O
of	O
the	O
m	O
counter	O
array	O
positions	O
,	O
generating	O
a	O
uniform	O
random	O
distribution	O
.	O
</s>
<s>
The	O
main	O
generalization	O
of	O
Bloom	B-Algorithm
filter	I-Algorithm
is	O
adding	O
an	O
element	O
.	O
</s>
<s>
To	O
add	O
an	O
element	O
,	O
feed	O
it	O
to	O
each	O
of	O
the	O
k	O
hash	B-Error_Name
functions	I-Error_Name
to	O
get	O
k	O
array	O
positions	O
and	O
increment	O
the	O
counters	O
1	O
at	O
all	O
these	O
positions	O
.	O
</s>
<s>
To	O
query	O
for	O
an	O
element	O
with	O
a	O
threshold	O
θ	O
(	O
test	O
whether	O
the	O
count	O
number	O
of	O
an	O
element	O
is	O
smaller	O
than	O
θ	O
)	O
,	O
feed	O
it	O
to	O
each	O
of	O
the	O
k	O
hash	B-Error_Name
functions	I-Error_Name
to	O
get	O
k	O
counter	O
positions	O
.	O
</s>
<s>
This	O
also	O
should	O
be	O
minimized	O
like	O
Bloom	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
About	O
hashing	O
problem	O
and	O
advantages	O
,	O
see	O
Bloom	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
A	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
is	O
essentially	O
the	O
same	O
data	B-General_Concept
structure	I-General_Concept
as	O
count	B-Algorithm
–	I-Algorithm
min	I-Algorithm
sketches	I-Algorithm
,	O
but	O
are	O
used	O
differently	O
.	O
</s>
<s>
Several	O
implementations	O
of	O
counting	B-Algorithm
bloom	I-Algorithm
filters	I-Algorithm
allow	O
for	O
deletion	O
,	O
by	O
decrementing	O
each	O
of	O
the	O
k	O
counters	O
for	O
a	O
given	O
input	O
.	O
</s>
<s>
The	O
same	O
assumptions	O
in	O
Bloom	B-Algorithm
filter	I-Algorithm
,	O
which	O
hash	B-Error_Name
functions	I-Error_Name
make	O
insertions	O
uniform	O
random	O
,	O
is	O
also	O
assumed	O
here	O
.	O
</s>
<s>
By	O
the	O
way	O
,	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
determines	O
an	O
element	O
is	O
greater	O
or	O
equal	O
to	O
θ	O
when	O
the	O
corresponding	O
k	O
counters	O
are	O
greater	O
or	O
equal	O
to	O
θ	O
.	O
</s>
<s>
This	O
is	O
different	O
from	O
formal	O
definition	O
of	O
false	O
positive	O
in	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
However	O
,	O
following	O
the	O
assumption	O
in	O
Bloom	B-Algorithm
filter	I-Algorithm
,	O
above	O
probability	O
is	O
defined	O
as	O
false	O
positive	O
of	O
counting	B-Algorithm
Bloom	I-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
If	O
θ	O
=	O
1	O
,	O
the	O
equation	O
becomes	O
false	O
positive	O
of	O
Bloom	B-Algorithm
filter	I-Algorithm
.	O
</s>
