<s>
Nets	B-Application
within	I-Application
Nets	I-Application
is	O
a	O
modelling	O
method	B-Language
belonging	O
to	O
the	O
family	O
of	O
Petri	B-Operating_System
nets	I-Operating_System
.	O
</s>
<s>
This	O
method	B-Language
is	O
distinguished	O
from	O
other	O
sorts	O
of	O
Petri	B-Operating_System
nets	I-Operating_System
by	O
the	O
possibility	O
to	O
provide	O
their	O
tokens	O
with	O
a	O
proper	O
structure	O
,	O
which	O
is	O
based	O
on	O
Petri	B-Operating_System
net	I-Operating_System
modelling	O
again	O
.	O
</s>
<s>
In	O
a	O
lot	O
of	O
publications	O
in	O
relation	O
to	O
object-oriented	B-Application
design	I-Application
is	O
given	O
,	O
in	O
order	O
to	O
combine	O
the	O
ability	O
of	O
Petri	B-Operating_System
nets	I-Operating_System
in	O
modelling	O
distributed	O
computing	O
with	O
the	O
modelling	O
of	O
objects	O
,	O
being	O
able	O
to	O
be	O
created	O
and	O
to	O
interact	O
.	O
</s>
<s>
some	O
of	O
these	O
approaches	O
,	O
namely	O
by	O
Sibertin-Blanc	O
,	O
Lakos	O
,	O
Moldt	O
und	O
Wienberg	O
as	O
extending	O
Coloured	O
Petri	B-Operating_System
nets	I-Operating_System
,	O
aside	O
the	O
Object	O
Nets	O
of	O
Valk	O
.	O
</s>
<s>
In	O
these	O
models	O
tasks	O
are	O
modelled	O
by	O
a	O
Petri	B-Operating_System
net	I-Operating_System
,	O
which	O
represents	O
the	O
precedences	O
of	O
tasks	O
and	O
their	O
state	O
of	O
execution	O
.	O
</s>
<s>
This	O
kind	O
of	O
semantic	O
is	O
distinguished	O
from	O
value	B-Application
semantics	I-Application
,	O
where	O
net	O
objects	O
may	O
exist	O
in	O
different	O
places	O
and	O
different	O
internal	O
states	O
.	O
</s>
<s>
In	O
value	B-Application
semantics	I-Application
different	O
copies	O
can	O
be	O
created	O
to	O
model	O
concurrent	O
execution	O
.	O
</s>
<s>
In	O
connection	O
with	O
mobile	O
computing	O
hybrid	O
versions	O
of	O
reference	O
and	O
value	B-Application
semantics	I-Application
are	O
of	O
importance	O
.	O
</s>
<s>
In	O
distributed	O
token	O
semantics	O
the	O
important	O
calculus	O
of	O
place	O
invariants	O
for	O
Petri	B-Operating_System
nets	I-Operating_System
remains	O
valid	O
.	O
</s>
<s>
The	O
formalism	O
of	O
nets	B-Application
within	I-Application
nets	I-Application
would	O
be	O
of	O
few	O
importance	O
without	O
communication	O
between	O
net	O
tokens	O
.	O
</s>
<s>
Like	O
in	O
object-oriented	B-Language
programming	I-Language
communication	O
of	O
net	O
tokens	O
is	O
introduced	O
via	O
predefined	O
interfaces	O
which	O
are	O
dynamically	O
bound	O
.	O
</s>
<s>
In	O
Figure	O
1	O
a	O
Petri	B-Operating_System
net	I-Operating_System
is	O
shown	O
containing	O
a	O
token	O
Petri	B-Operating_System
net	I-Operating_System
in	O
place	O
„a	O
“	O
.	O
</s>
<s>
The	O
channel	O
inscriptions	O
at	O
the	O
transitions	O
behave	O
like	O
a	O
call	O
of	O
a	O
method	B-Language
,	O
resulting	O
in	O
the	O
synchronised	O
firing	O
of	O
the	O
calling	O
transition	O
in	O
the	O
outer	O
net	O
[	O
e.g.	O
</s>
<s>
This	O
example	O
is	O
so	O
simple	O
that	O
reference	O
and	O
value	B-Application
semantics	I-Application
coincide	O
.	O
</s>
<s>
Standard	O
Petri	B-Operating_System
net	I-Operating_System
properties	O
like	O
reachability	B-Operating_System
,	O
boundedness	B-Operating_System
and	O
liveness	B-Operating_System
show	O
a	O
mixed	O
picture	O
.	O
</s>
<s>
A	O
paper	O
of	O
Köhler-Bußmeier	O
gives	O
a	O
survey	O
on	O
decidability	O
results	O
for	O
elementary	O
object	B-Language
systems	I-Language
.	O
</s>
<s>
To	O
reduce	O
the	O
complexity	O
of	O
the	O
formalism	O
subclasses	O
have	O
been	O
defined	O
by	O
restricting	O
the	O
structure	O
of	O
the	O
Petri	B-Operating_System
nets	I-Operating_System
,	O
as	O
for	O
instance	O
to	O
state	O
machines	O
.	O
</s>
<s>
Such	O
restrictions	O
still	O
allow	O
complex	O
modelling	O
of	O
distributed	O
and	O
mobile	O
systems	O
,	O
but	O
have	O
polynomial	O
complexity	O
in	O
model	B-Application
checking	I-Application
.	O
</s>
