<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
specifically	O
in	O
the	O
field	O
of	O
formal	O
verification	O
,	O
well-structured	B-Application
transition	I-Application
systems	I-Application
(	O
WSTSs	O
)	O
are	O
a	O
general	O
class	O
of	O
infinite	O
state	O
systems	O
for	O
which	O
many	O
verification	O
problems	O
are	O
decidable	O
,	O
owing	O
to	O
the	O
existence	O
of	O
a	O
kind	O
of	O
order	O
between	O
the	O
states	O
of	O
the	O
system	O
which	O
is	O
compatible	O
with	O
the	O
transitions	O
of	O
the	O
system	O
.	O
</s>
<s>
WSTS	O
decidability	O
results	O
can	O
be	O
applied	O
to	O
Petri	B-Operating_System
nets	I-Operating_System
,	O
lossy	O
channel	O
systems	O
,	O
and	O
more	O
.	O
</s>
<s>
For	O
our	O
purposes	O
,	O
a	O
transition	B-Application
system	I-Application
is	O
a	O
structure	O
,	O
where	O
is	O
any	O
set	O
(	O
its	O
elements	O
are	O
called	O
states	O
)	O
,	O
and	O
(	O
its	O
elements	O
are	O
called	O
transitions	O
)	O
.	O
</s>
<s>
In	O
general	O
a	O
transition	B-Application
system	I-Application
may	O
have	O
additional	O
structure	O
like	O
initial	O
states	O
,	O
labels	O
on	O
transitions	O
,	O
accepting	O
states	O
,	O
etc	O
.	O
</s>
<s>
A	O
well-structured	O
system	O
is	O
a	O
transition	B-Application
system	I-Application
with	O
state	O
set	O
made	O
up	O
from	O
a	O
finite	O
control	O
state	O
set	O
,	O
a	O
data	O
values	O
set	O
,	O
furnished	O
with	O
a	O
decidable	O
pre-order	O
which	O
is	O
extended	O
to	O
states	O
by	O
,	O
which	O
is	O
well-structured	O
as	O
defined	O
above	O
(	O
is	O
monotonic	O
,	O
i.e.	O
</s>
<s>
Well-structured	O
systems	O
adapt	O
the	O
theory	O
of	O
well-structured	B-Application
transition	I-Application
systems	I-Application
for	O
modelling	O
certain	O
classes	O
of	O
systems	O
encountered	O
in	O
computer	B-General_Concept
science	I-General_Concept
and	O
provide	O
the	O
basis	O
for	O
decision	O
procedures	O
to	O
analyse	O
such	O
systems	O
,	O
hence	O
the	O
supplementary	O
requirements	O
:	O
the	O
definition	O
of	O
a	O
WSTS	O
itself	O
says	O
nothing	O
about	O
the	O
computability	O
of	O
the	O
relations	O
,	O
.	O
</s>
<s>
in	O
the	O
case	O
of	O
unbounded	O
Petri	B-Operating_System
nets	I-Operating_System
)	O
by	O
a	O
forward	O
analysis	O
based	O
on	O
a	O
Karp-Miller	O
coverability	O
graph	O
.	O
</s>
