<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
retrieval	B-Application
data	I-Application
structure	I-Application
,	O
also	O
known	O
as	O
static	O
function	O
,	O
is	O
a	O
space-efficient	O
dictionary-like	O
data	O
type	O
composed	O
of	O
a	O
collection	O
of	O
(	O
key	O
,	O
value	O
)	O
pairs	O
that	O
allows	O
the	O
following	O
operations	O
:	O
</s>
<s>
In	O
contrast	O
to	O
static	O
functions	O
,	O
AMQ-filters	O
support	O
(	O
probabilistic	O
)	O
membership	O
queries	O
and	O
dictionaries	B-Application
additionally	O
allow	O
operations	O
like	O
listing	O
keys	O
or	O
looking	O
up	O
the	O
value	O
associated	O
with	O
a	O
key	O
and	O
returning	O
some	O
other	O
symbol	O
if	O
the	O
key	O
is	O
not	O
contained	O
.	O
</s>
<s>
As	O
can	O
be	O
derived	O
from	O
the	O
operations	O
,	O
this	O
data	O
structure	O
does	O
not	O
need	O
to	O
store	O
the	O
keys	O
at	O
all	O
and	O
may	O
actually	O
use	O
less	O
space	O
than	O
would	O
be	O
needed	O
for	O
a	O
simple	O
list	O
of	O
the	O
key	B-Application
value	I-Application
pairs	I-Application
.	O
</s>
<s>
Another	O
simple	O
example	O
to	O
build	O
a	O
static	O
function	O
is	O
using	O
a	O
perfect	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
:	O
After	O
building	O
the	O
PHF	O
for	O
our	O
keys	O
,	O
store	O
the	O
corresponding	O
values	O
at	O
the	O
correct	O
position	O
for	O
the	O
key	O
.	O
</s>
<s>
The	O
correctness	O
follows	O
from	O
the	O
correctness	O
of	O
the	O
perfect	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
Using	O
a	O
minimum	O
perfect	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
gives	O
a	O
big	O
space	O
improvement	O
if	O
the	O
associated	O
values	O
are	O
relatively	O
small	O
.	O
</s>
<s>
counting	B-Algorithm
sort	I-Algorithm
)	O
.	O
</s>
<s>
Row	O
operations	O
do	O
not	O
produce	O
any	O
values	O
outside	O
of	O
the	O
ribbon	O
and	O
are	O
very	O
cheap	O
since	O
they	O
only	O
require	O
an	O
XOR	O
of	O
bits	O
which	O
can	O
be	O
done	O
in	O
time	O
on	O
a	O
RAM	B-Application
.	O
</s>
<s>
A	O
retrieval	B-Application
data	I-Application
structure	I-Application
can	O
be	O
used	O
to	O
construct	O
a	O
perfect	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
:	O
First	O
insert	O
the	O
keys	O
into	O
a	O
cuckoo	O
hash	O
table	O
with	O
hash	O
functions	O
and	O
buckets	O
of	O
size	O
1	O
.	O
</s>
<s>
Then	O
,	O
for	O
every	O
key	O
store	O
the	O
index	O
of	O
the	O
hash	O
function	O
that	O
lead	O
to	O
a	O
key	O
's	O
insertion	O
into	O
the	O
hash	O
table	O
in	O
a	O
-bit	O
retrieval	B-Application
data	I-Application
structure	I-Application
.	O
</s>
<s>
The	O
perfect	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
is	O
given	O
by	O
.	O
</s>
