<s>
In	O
computational	O
complexity	O
theory	O
,	O
a	O
log-space	B-Algorithm
reduction	I-Algorithm
is	O
a	O
reduction	B-Algorithm
computable	O
by	O
a	O
deterministic	B-Architecture
Turing	I-Architecture
machine	I-Architecture
using	O
logarithmic	O
space	O
.	O
</s>
<s>
Formally	O
,	O
this	O
reduction	B-Algorithm
is	O
executed	O
via	O
a	O
log-space	O
transducer	O
.	O
</s>
<s>
Such	O
a	O
machine	O
has	O
polynomially-many	O
configurations	O
,	O
so	O
log-space	B-Algorithm
reductions	I-Algorithm
are	O
also	O
polynomial-time	B-Algorithm
reductions	I-Algorithm
.	O
</s>
<s>
However	O
,	O
log-space	B-Algorithm
reductions	I-Algorithm
are	O
probably	O
weaker	O
than	O
polynomial-time	B-Algorithm
reductions	I-Algorithm
;	O
while	O
any	O
non-empty	O
,	O
non-full	O
language	O
in	O
P	O
is	O
polynomial-time	O
reducible	B-Algorithm
to	O
any	O
other	O
non-empty	O
,	O
non-full	O
language	O
in	O
P	O
,	O
a	O
log-space	B-Algorithm
reduction	I-Algorithm
from	O
an	O
NL-complete	O
language	O
to	O
a	O
language	O
in	O
L	O
,	O
both	O
of	O
which	O
would	O
be	O
languages	O
in	O
P	O
,	O
would	O
imply	O
the	O
unlikely	O
L	O
=	O
NL	O
.	O
</s>
<s>
It	O
is	O
an	O
open	O
question	O
if	O
the	O
NP-complete	O
problems	O
are	O
different	O
with	O
respect	O
to	O
log-space	O
and	O
polynomial-time	B-Algorithm
reductions	I-Algorithm
.	O
</s>
<s>
Log-space	B-Algorithm
reductions	I-Algorithm
are	O
normally	O
used	O
on	O
languages	O
in	O
P	O
,	O
in	O
which	O
case	O
it	O
usually	O
does	O
not	O
matter	O
whether	O
many-one	B-Algorithm
reductions	I-Algorithm
or	O
Turing	B-Algorithm
reductions	I-Algorithm
are	O
used	O
,	O
since	O
it	O
has	O
been	O
verified	O
that	O
L	O
,	O
SL	O
,	O
NL	O
,	O
and	O
P	O
are	O
all	O
closed	O
under	O
Turing	B-Algorithm
reductions	I-Algorithm
,	O
meaning	O
that	O
Turing	B-Algorithm
reductions	I-Algorithm
can	O
be	O
used	O
to	O
show	O
a	O
problem	O
is	O
in	O
any	O
of	O
these	O
classes	O
.	O
</s>
<s>
However	O
,	O
other	O
subclasses	O
of	O
P	O
such	O
as	O
NC	O
may	O
not	O
be	O
closed	O
under	O
Turing	B-Algorithm
reductions	I-Algorithm
,	O
and	O
so	O
many-one	B-Algorithm
reductions	I-Algorithm
must	O
be	O
used	O
.	O
</s>
<s>
Just	O
as	O
polynomial-time	B-Algorithm
reductions	I-Algorithm
are	O
useless	O
within	O
P	O
and	O
its	O
subclasses	O
,	O
log-space	B-Algorithm
reductions	I-Algorithm
are	O
useless	O
to	O
distinguish	O
problems	O
in	O
L	O
and	O
its	O
subclasses	O
;	O
in	O
particular	O
,	O
every	O
non-empty	O
,	O
non-full	O
problem	O
in	O
L	O
is	O
trivially	O
L-complete	O
under	O
log-space	B-Algorithm
reductions	I-Algorithm
.	O
</s>
<s>
The	O
tools	O
available	O
to	O
designers	O
of	O
log-space	B-Algorithm
reductions	I-Algorithm
have	O
been	O
greatly	O
expanded	O
by	O
the	O
result	O
that	O
L	O
=	O
SL	O
;	O
see	O
SL	O
for	O
a	O
list	O
of	O
some	O
SL-complete	O
problems	O
that	O
can	O
now	O
be	O
used	O
as	O
subroutines	O
in	O
log-space	B-Algorithm
reductions	I-Algorithm
.	O
</s>
