<s>
A	O
logical	B-Operating_System
clock	I-Operating_System
is	O
a	O
mechanism	O
for	O
capturing	O
chronological	O
and	O
causal	O
relationships	O
in	O
a	O
distributed	B-Architecture
system	I-Architecture
.	O
</s>
<s>
Often	O
,	O
distributed	B-Architecture
systems	I-Architecture
may	O
have	O
no	O
physically	O
synchronous	O
global	O
clock	O
.	O
</s>
<s>
In	O
many	O
applications	O
(	O
such	O
as	O
distributed	O
GNU	O
make	O
)	O
,	O
if	O
two	O
processes	O
never	O
interact	O
,	O
the	O
lack	O
of	O
synchronization	O
is	O
unobservable	O
and	O
in	O
these	O
applications	O
it	O
is	O
enough	O
for	O
the	O
processes	O
to	O
agree	O
on	O
the	O
event	O
ordering	O
(	O
i.e.	O
,	O
logical	B-Operating_System
clock	I-Operating_System
)	O
rather	O
than	O
the	O
wall-clock	O
time	O
.	O
</s>
<s>
The	O
first	O
logical	B-Operating_System
clock	I-Operating_System
implementation	O
,	O
the	O
Lamport	B-Operating_System
timestamps	I-Operating_System
,	O
was	O
proposed	O
by	O
Leslie	O
Lamport	O
in	O
1978	O
(	O
Turing	O
Award	O
in	O
2013	O
)	O
.	O
</s>
<s>
In	O
logical	B-Operating_System
clock	I-Operating_System
systems	O
each	O
process	O
has	O
two	O
data	O
structures	O
:	O
logical	O
local	O
time	O
and	O
logical	O
global	O
time	O
.	O
</s>
<s>
Logical	B-Operating_System
clocks	I-Operating_System
are	O
useful	O
in	O
computation	O
analysis	O
,	O
distributed	O
algorithm	O
design	O
,	O
individual	O
event	O
tracking	O
,	O
and	O
exploring	O
computational	O
progress	O
.	O
</s>
<s>
Some	O
noteworthy	O
logical	B-Operating_System
clock	I-Operating_System
algorithms	I-Operating_System
are	O
:	O
</s>
<s>
Lamport	B-Operating_System
timestamps	I-Operating_System
,	O
which	O
are	O
monotonically	O
increasing	O
software	O
counters	O
.	O
</s>
<s>
Vector	B-Operating_System
clocks	I-Operating_System
,	O
that	O
allow	O
for	O
partial	O
ordering	O
of	O
events	O
in	O
a	O
distributed	B-Architecture
system	I-Architecture
.	O
</s>
<s>
Version	B-Operating_System
vectors	I-Operating_System
,	O
order	O
replicas	O
,	O
according	O
to	O
updates	O
,	O
in	O
an	O
optimistic	B-General_Concept
replicated	I-General_Concept
system	I-General_Concept
.	O
</s>
<s>
Matrix	B-Operating_System
clocks	I-Operating_System
,	O
an	O
extension	O
of	O
vector	B-Operating_System
clocks	I-Operating_System
that	O
also	O
contains	O
information	O
about	O
other	O
processes	O
 '	O
views	O
of	O
the	O
system	O
.	O
</s>
