<s>
A	O
vector	B-Application
addition	I-Application
system	I-Application
(	O
VAS	O
)	O
is	O
one	O
of	O
several	O
mathematical	O
modeling	O
languages	O
for	O
the	O
description	O
of	O
distributed	B-Architecture
systems	I-Architecture
.	O
</s>
<s>
Vector	B-Application
addition	I-Application
systems	I-Application
were	O
introduced	O
by	O
Richard	O
M	O
.	O
Karp	O
and	O
Raymond	O
E	O
.	O
Miller	O
in	O
1969	O
,	O
and	O
generalized	O
to	O
vector	B-Application
addition	I-Application
systems	I-Application
with	O
states	O
(	O
VASS	O
)	O
by	O
John	O
E	O
.	O
Hopcroft	O
and	O
Jean-Jacques	O
Pansiot	O
in	O
1979	O
.	O
</s>
<s>
Both	O
VAS	O
and	O
VASS	O
are	O
equivalent	O
in	O
many	O
ways	O
to	O
Petri	B-Operating_System
nets	I-Operating_System
introduced	O
earlier	O
by	O
Carl	O
Adam	O
Petri	O
.	O
</s>
<s>
Reachability	O
in	O
vector	B-Application
addition	I-Application
systems	I-Application
is	O
Ackermann-complete	O
(	O
and	O
hence	O
nonelementary	O
)	O
.	O
</s>
<s>
A	O
vector	B-Application
addition	I-Application
system	I-Application
consists	O
of	O
a	O
finite	O
set	O
of	O
integer	O
vectors	O
.	O
</s>
<s>
A	O
vector	B-Application
addition	I-Application
system	I-Application
with	I-Application
states	I-Application
is	O
a	O
VAS	O
equipped	O
with	O
control	O
states	O
.	O
</s>
