<s>
In	O
distributed	O
computing	O
,	O
shared-memory	B-Operating_System
systems	O
and	O
message-passing	B-Architecture
systems	O
are	O
two	O
means	O
of	O
interprocess	O
communication	O
which	O
have	O
been	O
heavily	O
studied	O
.	O
</s>
<s>
In	O
shared-memory	B-Operating_System
systems	O
,	O
processes	O
communicate	O
by	O
accessing	O
shared	B-Operating_System
data	I-Operating_System
structures	O
.	O
</s>
<s>
A	O
shared	O
(	O
read/write	O
)	O
register	O
,	O
sometimes	O
just	O
called	O
a	O
register	O
,	O
is	O
a	O
fundamental	O
type	O
of	O
shared	B-Operating_System
data	I-Operating_System
structure	O
which	O
stores	O
a	O
value	O
and	O
has	O
two	O
operations	O
:	O
read	O
,	O
which	O
returns	O
the	O
value	O
stored	O
in	O
the	O
register	O
,	O
and	O
write	O
,	O
which	O
updates	O
the	O
value	O
stored	O
.	O
</s>
<s>
Other	O
types	O
of	O
shared	B-Operating_System
data	I-Operating_System
structures	O
include	O
read	O
–	O
modify	O
–	O
write	O
,	O
test-and-set	O
,	O
compare-and-swap	O
etc	O
.	O
</s>
<s>
Registers	O
can	O
be	O
classified	O
according	O
to	O
the	O
consistency	B-General_Concept
condition	I-General_Concept
they	O
satisfy	O
when	O
accessed	O
concurrently	O
,	O
the	O
domain	O
of	O
possible	O
values	O
that	O
can	O
be	O
stored	O
,	O
and	O
how	O
many	O
processes	O
can	O
access	O
with	O
the	O
read	O
or	O
write	O
operation	O
,	O
which	O
leads	O
to	O
in	O
total	O
24	O
register	O
types	O
.	O
</s>
<s>
Lamport	O
defined	O
three	O
types	O
of	O
registers	O
:	O
safe	B-Operating_System
registers	I-Operating_System
,	O
regular	B-Operating_System
registers	O
and	O
atomic	B-General_Concept
registers	O
.	O
</s>
<s>
A	O
read	O
operation	O
of	O
a	O
safe	B-Operating_System
register	I-Operating_System
can	O
return	O
any	O
value	O
if	O
it	O
is	O
concurrent	O
with	O
a	O
Write	O
operation	O
,	O
and	O
returns	O
the	O
value	O
written	O
by	O
the	O
most	O
recent	O
write	O
operation	O
if	O
the	O
read	O
operation	O
does	O
not	O
overlap	O
with	O
any	O
write	O
.	O
</s>
<s>
A	O
regular	B-Operating_System
register	O
differs	O
from	O
a	O
safe	B-Operating_System
register	I-Operating_System
in	O
that	O
the	O
read	O
operation	O
can	O
return	O
the	O
value	O
written	O
by	O
either	O
the	O
most	O
recent	O
completed	O
Write	O
operation	O
or	O
a	O
Write	O
operation	O
it	O
overlaps	O
with	O
.	O
</s>
<s>
An	O
atomic	B-General_Concept
register	O
satisfies	O
the	O
stronger	O
condition	O
of	O
being	O
linearizable	B-General_Concept
.	O
</s>
<s>
The	O
figure	O
below	O
illustrates	O
the	O
constructions	O
stage	O
by	O
stage	O
from	O
the	O
implementation	O
of	O
SWSR	O
register	O
in	O
an	O
asynchronous	B-Application
message-passing	B-Architecture
system	O
to	O
the	O
implementation	O
of	O
MWMR	O
register	O
using	O
a	O
SW	B-Operating_System
Snapshot	I-Operating_System
object	I-Operating_System
.	O
</s>
<s>
There	O
is	O
an	O
article	O
which	O
discusses	O
the	O
details	O
of	O
constructing	O
snapshot	B-Operating_System
objects	I-Operating_System
.	O
</s>
<s>
An	O
implementation	O
is	O
linearizable	B-General_Concept
if	O
,	O
for	O
every	O
execution	O
there	O
is	O
a	O
linearization	O
ordering	O
that	O
satisfies	O
the	O
following	O
two	O
properties	O
:	O
</s>
<s>
A	O
SWSR	O
atomic	B-General_Concept
(	O
linearizable	B-General_Concept
)	O
register	O
can	O
be	O
implemented	O
in	O
an	O
asynchronous	B-Application
message-passing	B-Architecture
system	O
,	O
even	O
if	O
processes	O
may	O
crash	O
.	O
</s>
<s>
We	O
can	O
check	O
that	O
the	O
implementation	O
is	O
linearizable	B-General_Concept
.	O
</s>
<s>
We	O
can	O
use	O
the	O
a	O
SW	B-Operating_System
Snapshot	I-Operating_System
object	I-Operating_System
of	O
size	O
n	O
to	O
construct	O
a	O
MWMR	O
register	O
.	O
</s>
