<s>
Self-stabilization	B-Operating_System
is	O
a	O
concept	O
of	O
fault-tolerance	B-General_Concept
in	O
distributed	B-Architecture
systems	I-Architecture
.	O
</s>
<s>
Given	O
any	O
initial	O
state	B-Application
,	O
a	O
self-stabilizing	B-Operating_System
distributed	I-Operating_System
system	I-Operating_System
will	O
end	O
up	O
in	O
a	O
correct	O
state	B-Application
in	O
a	O
finite	O
number	O
of	O
execution	B-General_Concept
steps	O
.	O
</s>
<s>
At	O
first	O
glance	O
,	O
the	O
guarantee	O
of	O
self	O
stabilization	O
may	O
seem	O
less	O
promising	O
than	O
that	O
of	O
the	O
more	O
traditional	O
fault-tolerance	B-General_Concept
of	O
algorithms	O
,	O
that	O
aim	O
to	O
guarantee	O
that	O
the	O
system	O
always	O
remains	O
in	O
a	O
correct	O
state	B-Application
under	O
certain	O
kinds	O
of	O
state	B-Application
transitions	O
.	O
</s>
<s>
However	O
,	O
that	O
traditional	O
fault	B-General_Concept
tolerance	I-General_Concept
cannot	O
always	O
be	O
achieved	O
.	O
</s>
<s>
For	O
example	O
,	O
it	O
cannot	O
be	O
achieved	O
when	O
the	O
system	O
is	O
started	O
in	O
an	O
incorrect	O
state	B-Application
or	O
is	O
corrupted	O
by	O
an	O
intruder	O
.	O
</s>
<s>
Moreover	O
,	O
because	O
of	O
their	O
complexity	O
,	O
it	O
is	O
very	O
hard	O
to	O
debug	O
and	O
to	O
analyze	O
distributed	B-Architecture
systems	I-Architecture
.	O
</s>
<s>
Hence	O
,	O
it	O
is	O
very	O
hard	O
to	O
prevent	O
a	O
distributed	B-Architecture
system	I-Architecture
from	O
reaching	O
an	O
incorrect	O
state	B-Application
.	O
</s>
<s>
Indeed	O
,	O
some	O
forms	O
of	O
self-stabilization	B-Operating_System
are	O
incorporated	O
into	O
many	O
modern	O
computer	B-Architecture
and	O
telecommunications	O
networks	O
,	O
since	O
it	O
gives	O
them	O
the	O
ability	O
to	O
cope	O
with	O
faults	O
that	O
were	O
not	O
foreseen	O
in	O
the	O
design	O
of	O
the	O
algorithm	O
.	O
</s>
<s>
Many	O
years	O
after	O
the	O
seminal	O
paper	O
of	O
Edsger	O
Dijkstra	O
in	O
1974	O
,	O
this	O
concept	O
remains	O
important	O
as	O
it	O
presents	O
an	O
important	O
foundation	O
for	O
self-managing	B-General_Concept
computer	I-General_Concept
systems	I-General_Concept
and	O
fault-tolerant	B-General_Concept
systems	I-General_Concept
.	O
</s>
<s>
As	O
a	O
result	O
,	O
Dijkstra	O
's	O
paper	O
received	O
the	O
2002	O
ACM	O
PODC	O
Influential-Paper	O
Award	O
,	O
one	O
of	O
the	O
highest	O
recognitions	O
in	O
the	O
distributed	B-Architecture
computing	I-Architecture
community	O
.	O
</s>
<s>
Dijkstra	O
in	O
1974	O
presented	O
the	O
concept	O
of	O
self-stabilization	B-Operating_System
,	O
prompting	O
further	O
research	O
in	O
this	O
area	O
.	O
</s>
<s>
His	O
demonstration	O
involved	O
the	O
presentation	O
of	O
self-stabilizing	O
mutual	B-Operating_System
exclusion	I-Operating_System
algorithms	O
.	O
</s>
<s>
It	O
also	O
showed	O
the	O
first	O
self-stabilizing	B-Operating_System
algorithms	I-Operating_System
that	O
did	O
not	O
rely	O
on	O
strong	O
assumptions	O
on	O
the	O
system	O
.	O
</s>
<s>
It	O
was	O
only	O
ten	O
years	O
later	O
when	O
Leslie	O
Lamport	O
pointed	O
out	O
the	O
importance	O
of	O
Dijkstra	O
's	O
work	O
at	O
a	O
1983	O
conference	O
called	O
Symposium	O
on	O
Principles	O
of	O
Distributed	B-Architecture
Computing	I-Architecture
that	O
researchers	O
directed	O
their	O
attention	O
to	O
this	O
elegant	O
fault-tolerance	B-General_Concept
concept	O
.	O
</s>
<s>
I	O
regard	O
it	O
to	O
be	O
a	O
milestone	O
in	O
work	O
on	O
fault	B-General_Concept
tolerance	I-General_Concept
...	O
</s>
<s>
I	O
regard	O
self-stabilization	B-Operating_System
to	O
be	O
a	O
very	O
important	O
concept	O
in	O
fault	B-General_Concept
tolerance	I-General_Concept
and	O
to	O
be	O
a	O
very	O
fertile	O
field	O
for	O
research.Afterwards	O
,	O
Dijkstra	O
's	O
work	O
was	O
awarded	O
ACM-PODC	O
influential	O
paper	O
award	O
,	O
which	O
then	O
became	O
ACM	O
's	O
(	O
the	O
Association	O
for	O
computing	O
Machinery	O
)	O
Dijkstra	O
Prize	O
in	O
Distributed	B-Architecture
Computing	I-Architecture
given	O
at	O
the	O
annual	O
ACM-PODC	O
symposium	O
.	O
</s>
<s>
A	O
distributed	B-Operating_System
algorithm	I-Operating_System
is	O
self-stabilizing	O
if	O
,	O
starting	O
from	O
an	O
arbitrary	O
state	B-Application
,	O
it	O
is	O
guaranteed	O
to	O
converge	O
to	O
a	O
legitimate	O
state	B-Application
and	O
remain	O
in	O
a	O
legitimate	O
set	O
of	O
states	O
thereafter	O
.	O
</s>
<s>
A	O
state	B-Application
is	O
legitimate	O
if	O
,	O
starting	O
from	O
this	O
state	B-Application
,	O
the	O
algorithm	O
satisfies	O
its	O
specification	O
.	O
</s>
<s>
The	O
property	O
of	O
self-stabilization	B-Operating_System
enables	O
a	O
distributed	B-Operating_System
algorithm	I-Operating_System
to	O
recover	O
from	O
a	O
transient	O
fault	O
regardless	O
of	O
its	O
nature	O
.	O
</s>
<s>
Moreover	O
,	O
a	O
self-stabilizing	B-Operating_System
algorithm	I-Operating_System
does	O
not	O
have	O
to	O
be	O
initialized	O
as	O
it	O
eventually	O
starts	O
to	O
behave	O
correctly	O
regardless	O
of	O
its	O
initial	O
state	B-Application
.	O
</s>
<s>
Dijkstra	O
's	O
paper	O
,	O
which	O
introduces	O
the	O
concept	O
of	O
self-stabilization	B-Operating_System
,	O
presents	O
an	O
example	O
in	O
the	O
context	O
of	O
a	O
"	O
token	O
ring	O
"	O
a	O
network	O
of	O
computers	O
ordered	O
in	O
a	O
circle	O
.	O
</s>
<s>
Here	O
,	O
each	O
computer	B-Architecture
or	O
processor	O
can	O
"	O
see	O
"	O
the	O
whole	O
state	B-Application
of	O
one	O
processor	O
that	O
immediately	O
precedes	O
it	O
and	O
that	O
this	O
state	B-Application
may	O
imply	O
that	O
the	O
processor	O
"	O
has	O
a	O
token	O
"	O
or	O
it	O
"	O
does	O
not	O
have	O
a	O
token.	O
"	O
</s>
<s>
The	O
second	O
requirement	O
prescribes	O
that	O
each	O
node	O
"	O
passes	O
the	O
token	O
"	O
to	O
the	O
computer/processor	O
succeeding	O
it	O
so	O
that	O
the	O
token	O
eventually	O
circulates	O
the	O
ring	O
.	O
</s>
<s>
Not	O
holding	O
a	O
token	O
is	O
a	O
correct	O
state	B-Application
for	O
each	O
computer	B-Architecture
in	O
this	O
network	O
,	O
since	O
the	O
token	O
can	O
be	O
held	O
by	O
another	O
computer	B-Architecture
.	O
</s>
<s>
However	O
,	O
if	O
every	O
computer	B-Architecture
is	O
in	O
the	O
state	B-Application
of	O
"	O
not	O
holding	O
a	O
token	O
"	O
then	O
the	O
network	O
altogether	O
is	O
not	O
in	O
a	O
correct	O
state	B-Application
.	O
</s>
<s>
Similarly	O
,	O
if	O
more	O
than	O
one	O
computer	B-Architecture
"	O
holds	O
a	O
token	O
"	O
then	O
this	O
is	O
not	O
a	O
correct	O
state	B-Application
for	O
the	O
network	O
,	O
although	O
it	O
cannot	O
be	O
observed	O
to	O
be	O
incorrect	O
by	O
viewing	O
any	O
computer	B-Architecture
individually	O
.	O
</s>
<s>
Since	O
every	O
computer	B-Architecture
can	O
"	O
observe	O
"	O
only	O
the	O
states	O
of	O
its	O
two	O
neighbors	O
,	O
it	O
is	O
hard	O
for	O
the	O
computers	O
to	O
decide	O
whether	O
the	O
network	O
altogether	O
is	O
in	O
a	O
correct	O
state	B-Application
.	O
</s>
<s>
The	O
first	O
self-stabilizing	B-Operating_System
algorithms	I-Operating_System
did	O
not	O
detect	O
errors	O
explicitly	O
in	O
order	O
to	O
subsequently	O
repair	O
them	O
.	O
</s>
<s>
Instead	O
,	O
they	O
constantly	O
pushed	O
the	O
system	O
towards	O
a	O
legitimate	O
state	B-Application
.	O
</s>
<s>
(	O
The	O
method	O
described	O
in	O
the	O
paper	O
cited	O
above	O
collects	O
a	O
huge	O
amount	O
of	O
information	O
from	O
the	O
whole	O
network	O
to	O
one	O
place	O
;	O
after	O
that	O
,	O
it	O
attempts	O
to	O
determine	O
whether	O
the	O
collected	O
global	O
state	B-Application
is	O
correct	O
;	O
even	O
that	O
determination	O
alone	O
can	O
be	O
a	O
hard	O
task	O
)	O
.	O
</s>
<s>
More	O
recently	O
,	O
researchers	O
have	O
presented	O
newer	O
methods	O
for	O
light-weight	O
error	O
detection	O
for	O
self-stabilizing	B-Operating_System
systems	I-Operating_System
using	O
local	O
checking	O
.	O
</s>
<s>
The	O
term	O
local	O
refers	O
to	O
a	O
part	O
of	O
a	O
computer	B-Architecture
network	I-Architecture
.	O
</s>
<s>
When	O
local	O
detection	O
is	O
used	O
,	O
a	O
computer	B-Architecture
in	O
a	O
network	O
is	O
not	O
required	O
to	O
communicate	O
with	O
the	O
entire	O
network	O
in	O
order	O
to	O
detect	O
an	O
errorthe	O
error	O
can	O
be	O
detected	O
by	O
having	O
each	O
computer	B-Architecture
communicate	O
only	O
with	O
its	O
nearest	O
neighbors	O
.	O
</s>
<s>
These	O
local	O
detection	O
methods	O
simplified	O
the	O
task	O
of	O
designing	O
self-stabilizing	B-Operating_System
algorithms	I-Operating_System
considerably	O
.	O
</s>
<s>
detect	O
faults	O
(	O
during	O
the	O
execution	B-General_Concept
of	O
the	O
given	O
protocol	O
)	O
using	O
the	O
above-mentioned	O
detection	O
methods	O
,	O
</s>
<s>
then	O
,	O
apply	O
a	O
(	O
self	O
stabilizing	O
)	O
"	O
reset	O
"	O
protocol	O
to	O
return	O
the	O
system	O
to	O
some	O
predetermined	O
initial	O
state	B-Application
,	O
and	O
,	O
finally	O
,	O
</s>
<s>
Dijkstra	O
's	O
original	O
self-stabilization	B-Operating_System
algorithms	O
do	O
not	O
have	O
this	O
property	O
.	O
</s>
<s>
A	O
useful	O
property	O
of	O
self-stabilizing	B-Operating_System
algorithms	I-Operating_System
is	O
that	O
they	O
can	O
be	O
composed	O
of	O
layers	O
if	O
the	O
layers	O
do	O
not	O
exhibit	O
any	O
circular	B-Language
dependencies	I-Language
.	O
</s>
<s>
New	O
approaches	O
to	O
Dijkstra	O
's	O
work	O
emerged	O
later	O
on	O
such	O
as	O
the	O
case	O
of	O
Krzysztof	O
Apt	O
and	O
Ehsan	O
Shoja	O
's	O
proposition	O
,	O
which	O
demonstrated	O
how	O
self-stabilization	B-Operating_System
can	O
be	O
naturally	O
formulated	O
using	O
the	O
standard	O
concepts	O
of	O
strategic	O
games	O
,	O
particularly	O
the	O
concept	O
of	O
an	O
improvement	O
path	O
.	O
</s>
<s>
This	O
particular	O
work	O
sought	O
to	O
demonstrate	O
the	O
link	O
between	O
self-stabilization	B-Operating_System
and	O
game	O
theory	O
.	O
</s>
<s>
The	O
time	O
complexity	O
of	O
a	O
self-stabilizing	B-Operating_System
algorithm	I-Operating_System
is	O
measured	O
in	O
(	O
asynchronous	O
)	O
rounds	O
or	O
cycles	O
.	O
</s>
<s>
A	O
round	O
is	O
the	O
shortest	O
execution	B-General_Concept
trace	O
in	O
which	O
each	O
processor	O
executes	O
at	O
least	O
one	O
step	O
.	O
</s>
<s>
Similarly	O
,	O
a	O
cycle	O
is	O
the	O
shortest	O
execution	B-General_Concept
trace	O
in	O
which	O
each	O
processor	O
executes	O
at	O
least	O
one	O
complete	O
iteration	O
of	O
its	O
repeatedly	O
executed	O
list	O
of	O
commands	O
.	O
</s>
<s>
To	O
measure	O
the	O
output	O
stabilization	O
time	O
,	O
a	O
subset	O
of	O
the	O
state	B-Application
variables	O
is	O
defined	O
to	O
be	O
externally	O
visible	O
(	O
the	O
output	O
)	O
.	O
</s>
<s>
Starting	O
from	O
any	O
state	B-Application
,	O
it	O
is	O
guaranteed	O
that	O
the	O
system	O
will	O
eventually	O
reach	O
a	O
correct	O
state	B-Application
(	O
convergence	O
)	O
.	O
</s>
<s>
Given	O
that	O
the	O
system	O
is	O
in	O
a	O
correct	O
state	B-Application
,	O
it	O
is	O
guaranteed	O
to	O
stay	O
in	O
a	O
correct	O
state	B-Application
,	O
provided	O
that	O
no	O
fault	O
happens	O
(	O
closure	O
)	O
.	O
</s>
<s>
A	O
system	O
is	O
said	O
to	O
be	O
randomized	O
self-stabilizing	O
if	O
and	O
only	O
if	O
it	O
is	O
self-stabilizing	O
and	O
the	O
expected	O
number	O
of	O
rounds	O
needed	O
to	O
reach	O
a	O
correct	O
state	B-Application
is	O
bounded	O
by	O
some	O
constant	O
.	O
</s>
<s>
Design	O
of	O
self-stabilization	B-Operating_System
in	O
the	O
above-mentioned	O
sense	O
is	O
well	O
known	O
to	O
be	O
a	O
difficult	O
job	O
.	O
</s>
<s>
In	O
fact	O
,	O
a	O
class	O
of	O
distributed	B-Operating_System
algorithms	I-Operating_System
do	O
not	O
have	O
the	O
property	O
of	O
local	O
checking	O
:	O
the	O
legitimacy	O
of	O
the	O
network	O
state	B-Application
cannot	O
be	O
evaluated	O
by	O
a	O
single	O
process	O
.	O
</s>
<s>
The	O
most	O
obvious	O
case	O
is	O
Dijkstra	O
's	O
token-ring	O
defined	O
above	O
:	O
no	O
process	O
can	O
detect	O
whether	O
the	O
network	O
state	B-Application
is	O
legitimate	O
or	O
not	O
in	O
the	O
case	O
where	O
more	O
than	O
one	O
token	O
is	O
present	O
in	O
non-neighboring	O
processes	O
.	O
</s>
<s>
This	O
suggests	O
that	O
self-stabilization	B-Operating_System
of	O
a	O
distributed	B-Architecture
system	I-Architecture
is	O
a	O
sort	O
of	O
collective	O
intelligence	O
where	O
each	O
component	O
is	O
taking	O
local	O
actions	O
,	O
based	O
on	O
its	O
local	O
knowledge	O
but	O
eventually	O
this	O
guarantees	O
global	O
convergence	O
at	O
the	O
end	O
.	O
</s>
<s>
To	O
help	O
overcome	O
the	O
difficulty	O
of	O
designing	O
self-stabilization	B-Operating_System
as	O
defined	O
above	O
,	O
other	O
types	O
of	O
stabilization	O
were	O
devised	O
.	O
</s>
<s>
For	O
instance	O
,	O
weak	O
stabilization	O
is	O
the	O
property	O
that	O
a	O
distributed	B-Architecture
system	I-Architecture
has	O
a	O
possibility	O
to	O
reach	O
its	O
legitimate	O
behavior	O
from	O
every	O
possible	O
state	B-Application
.	O
</s>
<s>
Weak	O
stabilization	O
is	O
easier	O
to	O
design	O
as	O
it	O
just	O
guarantees	O
a	O
possibility	O
of	O
convergence	O
for	O
some	O
runs	O
of	O
the	O
distributed	B-Architecture
system	I-Architecture
rather	O
than	O
convergence	O
for	O
every	O
run	O
.	O
</s>
<s>
A	O
self-stabilizing	B-Operating_System
algorithm	I-Operating_System
is	O
silent	O
if	O
and	O
only	O
if	O
it	O
converges	O
to	O
a	O
global	O
state	B-Application
where	O
the	O
values	O
of	O
communication	O
registers	O
used	O
by	O
the	O
algorithm	O
remain	O
fixed	O
.	O
</s>
<s>
An	O
extension	O
of	O
the	O
concept	O
of	O
self-stabilization	B-Operating_System
is	O
that	O
of	O
superstabilization	B-Operating_System
.	O
</s>
<s>
The	O
intent	O
here	O
is	O
to	O
cope	O
with	O
dynamic	O
distributed	B-Architecture
systems	I-Architecture
that	O
undergo	O
topological	O
changes	O
.	O
</s>
<s>
In	O
classical	O
self-stabilization	B-Operating_System
theory	O
,	O
arbitrary	O
changes	O
are	O
viewed	O
as	O
errors	O
where	O
no	O
guarantees	O
are	O
given	O
until	O
the	O
system	O
has	O
stabilized	O
again	O
.	O
</s>
