<s>
In	O
computability	O
theory	O
,	O
a	O
truth-table	B-Algorithm
reduction	I-Algorithm
is	O
a	O
reduction	B-Algorithm
from	O
one	O
set	O
of	O
natural	O
numbers	O
to	O
another	O
.	O
</s>
<s>
As	O
a	O
"	O
tool	O
"	O
,	O
it	O
is	O
weaker	O
than	O
Turing	B-Algorithm
reduction	I-Algorithm
,	O
since	O
not	O
every	O
Turing	B-Algorithm
reduction	I-Algorithm
between	O
sets	O
can	O
be	O
performed	O
by	O
a	O
truth-table	B-Algorithm
reduction	I-Algorithm
,	O
but	O
every	O
truth-table	B-Algorithm
reduction	I-Algorithm
can	O
be	O
performed	O
by	O
a	O
Turing	B-Algorithm
reduction	I-Algorithm
.	O
</s>
<s>
For	O
the	O
same	O
reason	O
it	O
is	O
said	O
to	O
be	O
a	O
stronger	O
reducibility	O
than	O
Turing	B-Algorithm
reducibility	I-Algorithm
,	O
because	O
it	O
implies	O
Turing	B-Algorithm
reducibility	I-Algorithm
.	O
</s>
<s>
A	O
weak	O
truth-table	B-Algorithm
reduction	I-Algorithm
is	O
a	O
related	O
type	O
of	O
reduction	B-Algorithm
which	O
is	O
so	O
named	O
because	O
it	O
weakens	O
the	O
constraints	O
placed	O
on	O
a	O
truth-table	B-Algorithm
reduction	I-Algorithm
,	O
and	O
provides	O
a	O
weaker	O
equivalence	O
classification	O
;	O
as	O
such	O
,	O
a	O
"	O
weak	O
truth-table	B-Algorithm
reduction	I-Algorithm
"	O
can	O
actually	O
be	O
more	O
powerful	O
than	O
a	O
truth-table	B-Algorithm
reduction	I-Algorithm
as	O
a	O
"	O
tool	O
"	O
,	O
and	O
perform	O
a	O
reduction	B-Algorithm
which	O
is	O
not	O
performable	O
by	O
truth	O
table	O
.	O
</s>
<s>
A	O
Turing	B-Algorithm
reduction	I-Algorithm
from	O
a	O
set	O
B	O
to	O
a	O
set	O
A	O
computes	O
the	O
membership	O
of	O
a	O
single	O
element	O
in	O
B	O
by	O
asking	O
questions	O
about	O
the	O
membership	O
of	O
various	O
elements	O
in	O
A	O
during	O
the	O
computation	O
;	O
it	O
may	O
adaptively	O
determine	O
which	O
questions	O
it	O
asks	O
based	O
upon	O
answers	O
to	O
previous	O
questions	O
.	O
</s>
<s>
In	O
contrast	O
,	O
a	O
truth-table	B-Algorithm
reduction	I-Algorithm
or	O
a	O
weak	O
truth-table	B-Algorithm
reduction	I-Algorithm
must	O
present	O
all	O
of	O
its	O
(	O
finitely	O
many	O
)	O
oracle	O
queries	O
at	O
the	O
same	O
time	O
.	O
</s>
<s>
In	O
a	O
truth-table	B-Algorithm
reduction	I-Algorithm
,	O
the	O
reduction	B-Algorithm
also	O
gives	O
a	O
boolean	O
function	O
(	O
a	O
truth	O
table	O
)	O
which	O
,	O
when	O
given	O
the	O
answers	O
to	O
the	O
queries	O
,	O
will	O
produce	O
the	O
final	O
answer	O
of	O
the	O
reduction	B-Algorithm
.	O
</s>
<s>
In	O
a	O
weak	O
truth-table	B-Algorithm
reduction	I-Algorithm
,	O
the	O
reduction	B-Algorithm
uses	O
the	O
oracle	O
answers	O
as	O
a	O
basis	O
for	O
further	O
computation	O
which	O
may	O
depend	O
on	O
the	O
given	O
answers	O
but	O
may	O
not	O
ask	O
further	O
questions	O
of	O
the	O
oracle	O
.	O
</s>
<s>
Equivalently	O
,	O
a	O
weak	O
truth-table	B-Algorithm
reduction	I-Algorithm
is	O
a	O
Turing	B-Algorithm
reduction	I-Algorithm
for	O
which	O
the	O
use	O
of	O
the	O
reduction	B-Algorithm
is	O
bounded	O
by	O
a	O
computable	O
function	O
.	O
</s>
<s>
As	O
every	O
truth-table	B-Algorithm
reduction	I-Algorithm
is	O
a	O
Turing	B-Algorithm
reduction	I-Algorithm
,	O
if	O
A	O
is	O
truth-table	O
reducible	B-Algorithm
to	O
B	O
(	O
A	O
tt	O
B	O
)	O
,	O
then	O
A	O
is	O
also	O
Turing	B-Algorithm
reducible	I-Algorithm
to	O
B	O
(	O
A	O
T	O
B	O
)	O
.	O
</s>
<s>
or	O
in	O
other	O
words	O
,	O
one-one	O
reducibility	O
implies	O
many-one	O
reducibility	O
,	O
which	O
implies	O
truth-table	O
reducibility	O
,	O
which	O
in	O
turn	O
implies	O
weak	O
truth-table	O
reducibility	O
,	O
which	O
in	O
turn	O
implies	O
Turing	B-Algorithm
reducibility	I-Algorithm
.	O
</s>
<s>
Furthermore	O
,	O
A	O
is	O
truth-table	O
reducible	B-Algorithm
to	O
B	O
iff	O
A	O
is	O
Turing	B-Algorithm
reducible	I-Algorithm
to	O
B	O
via	O
a	O
total	O
functional	O
on	O
.	O
</s>
