<s>
A	O
virtual	B-Application
finite-state	I-Application
machine	I-Application
(	O
VFSM	B-Application
)	O
is	O
a	O
finite-state	B-Architecture
machine	I-Architecture
(	O
FSM	O
)	O
defined	O
in	O
a	O
Virtual	O
Environment	O
.	O
</s>
<s>
The	O
VFSM	B-Application
concept	O
provides	O
a	O
software	B-Application
specification	I-Application
method	O
to	O
describe	O
the	O
behaviour	O
of	O
a	O
control	O
system	O
using	O
assigned	O
names	O
of	O
input	B-General_Concept
control	I-General_Concept
properties	I-General_Concept
and	I-General_Concept
output	I-General_Concept
actions	I-General_Concept
.	O
</s>
<s>
The	O
VFSM	B-Application
method	O
introduces	O
an	O
execution	B-Device
model	I-Device
and	O
facilitates	O
the	O
idea	O
of	O
an	O
executable	O
specification	B-Application
.	O
</s>
<s>
This	O
technology	O
is	O
mainly	O
used	O
in	O
complex	O
machine	O
control	O
,	O
instrumentation	B-Application
,	O
and	O
telecommunication	O
applications	O
.	O
</s>
<s>
Implementing	O
a	O
state	B-Architecture
machine	I-Architecture
necessitates	O
the	O
generation	O
of	O
logical	O
conditions	O
(	O
state	B-Application
transition	I-Application
conditions	O
and	O
action	O
conditions	O
)	O
.	O
</s>
<s>
In	O
the	O
hardware	O
environment	O
,	O
where	O
state	B-Architecture
machines	I-Architecture
found	O
their	O
original	O
use	O
,	O
this	O
is	O
trivial	O
:	O
all	O
signals	O
are	O
Boolean	O
.	O
</s>
<s>
In	O
contrast	O
state	B-Architecture
machines	I-Architecture
specified	O
and	O
implemented	O
in	O
software	O
require	O
logical	O
conditions	O
that	O
are	O
per	O
se	O
multivalued	O
:	O
</s>
<s>
A	O
Positive	O
Logical	O
Algebra	O
solves	O
this	O
problem	O
via	O
virtualization	B-General_Concept
,	O
by	O
creating	O
a	O
Virtual	O
Environment	O
which	O
allows	O
specification	B-Application
of	O
state	B-Architecture
machines	I-Architecture
for	O
software	O
using	O
multivalued	O
variables	O
.	O
</s>
<s>
A	O
state	O
variable	O
in	O
the	O
VFSM	B-Application
environment	O
may	O
have	O
one	O
or	O
more	O
values	O
which	O
are	O
relevant	O
for	O
the	O
Control	O
—	O
in	O
such	O
a	O
case	O
it	O
is	O
an	O
input	O
variable	O
.	O
</s>
<s>
Control	O
properties	O
are	O
not	O
necessarily	O
specific	O
data	O
values	O
but	O
are	O
rather	O
certain	O
states	B-Application
of	O
the	O
variable	O
.	O
</s>
<s>
Other	O
state	O
variables	O
in	O
the	O
VFSM	B-Application
environment	O
may	O
be	O
activated	O
by	O
actions	O
—	O
in	O
such	O
a	O
case	O
it	O
is	O
an	O
output	O
variable	O
.	O
</s>
<s>
A	O
timer	O
which	O
is	O
both	O
:	O
an	O
input	B-General_Concept
and	I-General_Concept
output	I-General_Concept
variable	O
can	O
be	O
triggered	O
by	O
actions	O
like	O
:	O
Start	O
,	O
Stop	O
or	O
Reset	O
.	O
</s>
<s>
The	O
virtual	O
environment	O
characterises	O
the	O
runtime	B-Device
environment	I-Device
in	O
which	O
a	O
virtual	B-Architecture
machine	I-Architecture
operates	O
.	O
</s>
<s>
state	O
names	O
,	O
as	O
defined	O
for	O
each	O
of	O
the	O
states	B-Application
of	O
the	O
FSM	O
.	O
</s>
<s>
The	O
input	O
names	O
build	O
virtual	O
conditions	O
to	O
perform	O
state	B-Application
transitions	I-Application
or	O
input	O
actions	O
.	O
</s>
<s>
A	O
logical	O
expression	O
is	O
an	O
OR-table	O
of	O
AND-sets	O
(	O
a	O
disjunctive	B-Application
normal	I-Application
form	I-Application
)	O
:	O
</s>
<s>
This	O
is	O
built	O
by	O
the	O
current	O
action(s )	O
of	O
the	O
VFSM	B-Application
.	O
</s>
<s>
The	O
behaviour	O
specification	B-Application
is	O
built	O
by	O
a	O
state	B-Application
table	I-Application
which	O
describes	O
all	O
details	O
of	O
all	O
states	B-Application
of	O
the	O
VFSM	B-Application
.	O
</s>
<s>
The	O
VFSM	B-Application
executor	O
is	O
triggered	O
by	O
VI	O
and	O
the	O
current	O
state	O
of	O
the	O
VFSM	B-Application
.	O
</s>
<s>
In	O
consideration	O
of	O
the	O
behaviour	O
specification	B-Application
of	O
the	O
current	O
state	O
,	O
the	O
VO	O
is	O
set	O
.	O
</s>
<s>
Figure	O
2	O
shows	O
one	O
possible	O
implementation	O
of	O
a	O
VFSM	B-Application
executor	O
.	O
</s>
<s>
A	O
state	B-Application
table	I-Application
defines	O
all	O
details	O
of	O
the	O
behaviour	O
of	O
a	O
state	O
of	O
a	O
VFSM	B-Application
.	O
</s>
<s>
Finally	O
the	O
lines	O
providing	O
the	O
next	O
state	O
represent	O
the	O
state	B-Application
transition	I-Application
conditions	O
and	O
transition	O
actions	O
.	O
</s>
<s>
A	O
pure	O
combinatorial	O
VFSM	B-Application
is	O
possible	O
in	O
cases	O
only	O
where	O
input	O
actions	O
are	O
used	O
,	O
but	O
no	O
state	B-Application
transitions	I-Application
are	O
defined	O
.	O
</s>
