<s>
Regular	B-Operating_System
semantics	I-Operating_System
is	O
a	O
computing	O
term	O
which	O
describes	O
one	O
type	O
of	O
guarantee	O
provided	O
by	O
a	O
data	O
register	O
shared	O
by	O
several	O
processors	O
in	O
a	O
parallel	B-Operating_System
machine	I-Operating_System
or	O
in	O
a	O
network	B-Architecture
of	O
computers	O
working	O
together	O
.	O
</s>
<s>
Regular	B-Operating_System
semantics	I-Operating_System
are	O
defined	O
for	O
a	O
variable	O
with	O
a	O
single	O
writer	O
but	O
multiple	O
readers	O
.	O
</s>
<s>
These	O
semantics	O
are	O
stronger	O
than	O
safe	B-Operating_System
semantics	I-Operating_System
but	O
weaker	O
than	O
atomic	B-Operating_System
semantics	I-Operating_System
:	O
they	O
guarantee	O
that	O
there	O
is	O
a	O
total	O
order	O
to	O
the	O
write	O
operations	O
which	O
is	O
consistent	O
with	O
real-time	B-General_Concept
and	O
that	O
read	O
operations	O
return	O
either	O
the	O
value	O
of	O
the	O
last	O
write	O
completed	O
before	O
the	O
read	O
begins	O
,	O
or	O
that	O
of	O
one	O
of	O
the	O
writes	O
which	O
are	O
concurrent	B-Operating_System
with	O
the	O
read	O
.	O
</s>
<s>
Regular	B-Operating_System
semantics	I-Operating_System
are	O
weaker	O
than	O
linearizability	B-General_Concept
.	O
</s>
<s>
According	O
to	O
a	O
regular	O
register	O
's	O
definition	O
,	O
the	O
third	O
read	O
should	O
return	O
3	O
since	O
the	O
read	O
operation	O
is	O
not	O
concurrent	B-Operating_System
with	O
any	O
write	O
operation	O
.	O
</s>
<s>
This	O
behavior	O
would	O
not	O
satisfy	O
atomic	B-Operating_System
semantics	I-Operating_System
.	O
</s>
<s>
Therefore	O
,	O
regular	B-Operating_System
semantics	I-Operating_System
is	O
a	O
weaker	O
property	O
than	O
an	O
atomic	B-Operating_System
semantics	I-Operating_System
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
Leslie	O
Lamport	O
proved	O
that	O
a	O
linearizable	B-General_Concept
register	O
may	O
be	O
implemented	O
from	O
registers	O
with	O
safe	B-Operating_System
semantics	I-Operating_System
,	O
which	O
are	O
weaker	O
than	O
regular	O
registers	O
.	O
</s>
<s>
A	O
single-writer	O
multi-reader	O
(	O
SWMR	O
)	O
atomic	B-Operating_System
semantics	I-Operating_System
is	O
an	O
SWMR	O
regular	O
register	O
if	O
any	O
of	O
its	O
execution	O
history	O
H	O
satisfies	O
the	O
following	O
property	O
:	O
</s>
<s>
This	O
is	O
actually	O
the	O
main	O
difference	O
between	O
atomicity	B-General_Concept
and	O
regularity	O
.	O
</s>
<s>
For	O
proving	O
the	O
theorem	O
above	O
,	O
first	O
we	O
should	O
prove	O
that	O
the	O
register	O
is	O
safe	O
,	O
next	O
we	O
should	O
show	O
that	O
the	O
register	O
is	O
regular	O
,	O
and	O
then	O
at	O
the	O
end	O
we	O
should	O
show	O
that	O
the	O
register	O
does	O
not	O
allow	O
for	O
new/old	O
inversion	O
which	O
proves	O
the	O
atomicity	B-General_Concept
.	O
</s>
<s>
Furthermore	O
,	O
this	O
total	O
order	O
is	O
an	O
execution	O
of	O
M	O
only	O
adds	O
an	O
order	O
on	O
operations	O
that	O
are	O
overlapping	O
in	O
M	O
.	O
If	O
there	O
is	O
no	O
overlapping	O
between	O
a	O
read	O
and	O
write	O
operations	O
,	O
there	O
is	O
no	O
difference	O
between	O
the	O
regularity	O
and	O
atomicity	B-General_Concept
.	O
</s>
<s>
Therefore	O
,	O
the	O
corresponding	O
history	O
is	O
linearizable	B-General_Concept
.	O
</s>
<s>
Since	O
atomicity	B-General_Concept
(	O
linearizability	B-General_Concept
)	O
is	O
a	O
local	O
property	O
,	O
we	O
can	O
state	O
that	O
a	O
set	O
of	O
SWMR	O
regular	O
registers	O
behave	O
atomically	O
as	O
soon	O
as	O
each	O
of	O
them	O
satisfies	O
the	O
no	O
new/old	O
inversion	O
property	O
.	O
</s>
